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README.md

Deep Learning Tuning Playbook

Deep Learning Tuning Playbook

This is not an officially supported Google product.

Varun Godbole^†, George E. Dahl^†, Justin Gilmer^†, Christopher J. Shallue^‡, Zachary Nado^†

† Google Research, Brain Team

‡ Harvard University

Who is this document for?
Why a tuning playbook?
Guide for starting a new project
A scientific approach to improving model performance
Determining the number of steps for each training run
- Deciding how long to train when training is not compute-bound
- Deciding how long to train when training is compute-bound
Additional guidance for the training pipeline
FAQs
Acknowledgments
Citing
Contributing

Who is this document for?

This document is for engineers and researchers (both individuals and teams)
interested in maximizing the performance of deep learning models. We assume
basic knowledge of machine learning and deep learning concepts.

Our emphasis is on the process of hyperparameter tuning. We touch on other
aspects of deep learning training, such as pipeline implementation and
optimization, but our treatment of those aspects is not intended to be complete.

We assume the machine learning problem is a supervised learning problem or
something that looks a lot like one (e.g. self-supervised). That said, some of
the prescriptions in this document may also apply to other types of problems.

Why a tuning playbook?

Currently, there is an astonishing amount of toil and guesswork involved in
actually getting deep neural networks to work well in practice. Even worse, the
actual recipes people use to get good results with deep learning are rarely
documented. Papers gloss over the process that led to their final results in
order to present a cleaner story, and machine learning engineers working on
commercial problems rarely have time to take a step back and generalize their
process. Textbooks tend to eschew practical guidance and prioritize fundamental
principles, even if their authors have the necessary experience in applied work
to provide useful advice. When preparing to create this document, we couldn't
find any comprehensive attempt to actually explain how to get good results with
deep learning. Instead, we found snippets of advice in blog posts and on social
media, tricks peeking out of the appendix of research papers, occasional case
studies about one particular project or pipeline, and a lot of confusion. There
is a vast gulf between the results achieved by deep learning experts and less
skilled practitioners using superficially similar methods. At the same time,
these very experts readily admit some of what they do might not be
well-justified. As deep learning matures and has a larger impact on the world,
the community needs more resources covering useful recipes, including all the
practical details that can be so critical for obtaining good results.

We are a team of five researchers and engineers who have worked in deep learning
for many years, some of us since as early as 2006. We have applied deep learning
to problems in everything from speech recognition to astronomy, and learned a
lot along the way. This document grew out of our own experience training neural
networks, teaching new machine learning engineers, and advising our colleagues
on the practice of deep learning. Although it has been gratifying to see deep
learning go from a machine learning approach practiced by a handful of academic
labs to a technology powering products used by billions of people, deep learning
is still in its infancy as an engineering discipline and we hope this document
encourages others to help systematize the field's experimental protocols.

This document came about as we tried to crystalize our own approach to deep
learning and thus it represents the opinions of the authors at the time of
writing, not any sort of objective truth. Our own struggles with hyperparameter
tuning made it a particular focus of our guidance, but we also cover other
important issues we have encountered in our work (or seen go wrong). Our
intention is for this work to be a living document that grows and evolves as our
beliefs change. For example, the material on debugging and mitigating training
failures would not have been possible for us to write two years ago since it is
based on recent results and ongoing investigations. Inevitably, some of our
advice will need to be updated to account for new results and improved
workflows. We do not know the optimal deep learning recipe, but until the
community starts writing down and debating different procedures, we cannot hope
to find it. To that end, we would encourage readers who find issues with our
advice to produce alternative recommendations, along with convincing evidence,
so we can update the playbook. We would also love to see alternative guides and
playbooks that might have different recommendations so we can work towards best
practices as a community. Finally, any sections marked with a 🤖 emoji are places
we would like to do more research. Only after trying to write this playbook did
it become completely clear how many interesting and neglected research questions
can be found in the deep learning practitioner's workflow.

Guide for starting a new project

Many of the decisions we make over the course of tuning can be made once at the
beginning of a project and only occasionally revisited when circumstances
change.

Our guidance below makes the following assumptions:

Enough of the essential work of problem formulation, data cleaning, etc. has
already been done that spending time on the model architecture and training
configuration makes sense.
There is already a pipeline set up that does training and evaluation, and it
is easy to execute training and prediction jobs for various models of
interest.
The appropriate metrics have been selected and implemented. These should be
as representative as possible of what would be measured in the deployed
environment.

Choosing the model architecture

Summary: When starting a new project, try to reuse a model that already
works.

Choose a well established, commonly used model architecture to get working
first. It is always possible to build a custom model later.
Model architectures typically have various hyperparameters that determine
the model's size and other details (e.g. number of layers, layer width, type
of activation function).
- Thus, choosing the architecture really means choosing a family of
  different models (one for each setting of the model hyperparameters).
- We will consider the problem of choosing the model hyperparameters in
  Choosing the initial configuration
  and
  A scientific approach to improving model performance.
When possible, try to find a paper that tackles something as close as
possible to the problem at hand and reproduce that model as a starting
point.

Choosing the optimizer

Summary: Start with the most popular optimizer for the type of problem at
hand.

No optimizer is the "best" across all types of machine learning problems and
model architectures. Even just
comparing the performance of optimizers is a difficult task.
🤖
We recommend sticking with well-established, popular optimizers, especially
when starting a new project.
- Ideally, choose the most popular optimizer used for the same type of
  problem.
Be prepared to give attention to *all* hyperparameters of the
chosen optimizer.
- Optimizers with more hyperparameters may require more tuning effort to
  find the best configuration.
- This is particularly relevant in the beginning stages of a project when
  we are trying to find the best values of various other hyperparameters
  (e.g. architecture hyperparameters) while treating optimizer
  hyperparameters as
  nuisance parameters.
- It may be preferable to start with a simpler optimizer (e.g. SGD with
  fixed momentum or Adam with fixed $\epsilon$, $\beta_{1}$, and
  $\beta_{2}$) in the initial stages of the project and switch to a more
  general optimizer later.
Well-established optimizers that we like include (but are not limited to):
- SGD with momentum
  (we like the Nesterov variant)
- Adam and NAdam,
  which are more general than SGD with momentum. Note that Adam has 4
  tunable hyperparameters
  and they can all matter!
  - See
    How should Adam's hyperparameters be tuned?

Choosing the batch size

Summary: The batch size governs the training speed and shouldn't be used
to directly tune the validation set performance. Often, the ideal batch size
will be the largest batch size supported by the available hardware.

The batch size is a key factor in determining the training time and
computing resource consumption.
Increasing the batch size will often reduce the training time. This can be
highly beneficial because it, e.g.:
- Allows hyperparameters to be tuned more thoroughly within a fixed time
  interval, potentially resulting in a better final model.
- Reduces the latency of the development cycle, allowing new ideas to be
  tested more frequently.
Increasing the batch size may either decrease, increase, or not change the
resource consumption.
The batch size should not be treated as a tunable hyperparameter for
validation set performance.
- As long as all hyperparameters are well-tuned (especially the learning
  rate and regularization hyperparameters) and the number of training
  steps is sufficient, the same final performance should be attainable
  using any batch size (see
  Shallue et al. 2018).
- Please see Why shouldn't the batch size be tuned to directly improve
  validation set
  performance?

Determining the feasible batch sizes and estimating training throughput

[Click to expand]

For a given model and optimizer, there will typically be a range of batch
sizes supported by the available hardware. The limiting factor is usually
accelerator memory.
Unfortunately, it can be difficult to calculate which batch sizes will fit
in memory without running, or at least compiling, the full training program.
The easiest solution is usually to run training jobs at different batch
sizes (e.g. increasing powers of 2) for a small number of steps until one of
the jobs exceeds the available memory.
For each batch size, we should train for long enough to get a reliable
estimate of the training throughput

training throughput = (# examples processed per second)

or, equivalently, the time per step.

time per step = (batch size) / (training throughput)

When the accelerators aren't yet saturated, if the batch size doubles, the
training throughput should also double (or at least nearly double).
Equivalently, the time per step should be constant (or at least nearly
constant) as the batch size increases.
If this is not the case then the training pipeline has a bottleneck such as
I/O or synchronization between compute nodes. This may be worth diagnosing
and correcting before proceeding.
If the training throughput increases only up to some maximum batch size,
then we should only consider batch sizes up to that maximum batch size, even
if a larger batch size is supported by the hardware.
- All benefits of using a larger batch size assume the training throughput
  increases. If it doesn't, fix the bottleneck or use the smaller batch
  size.
- Gradient accumulation simulates a larger batch size than the
  hardware can support and therefore does not provide any throughput
  benefits. It should generally be avoided in applied work.
These steps may need to be repeated every time the model or optimizer is
changed (e.g. a different model architecture may allow a larger batch size
to fit in memory).

Choosing the batch size to minimize training time

[Click to expand]

Training time = (time per step) x (total number of steps)

We can often consider the time per step to be approximately constant for all
feasible batch sizes. This is true when there is no overhead from parallel
computations and all training bottlenecks have been diagnosed and corrected
(see the
previous section
for how to identify training bottlenecks). In practice, there is usually at
least some overhead from increasing the batch size.
As the batch size increases, the total number of steps needed to reach a
fixed performance goal typically decreases (provided all relevant
hyperparameters are re-tuned when the batch size is changed;
Shallue et al. 2018).
- E.g. Doubling the batch size might halve the total number of steps
  required. This is called perfect scaling.
- Perfect scaling holds for all batch sizes up to a critical batch size,
  beyond which one achieves diminishing returns.
- Eventually, increasing the batch size no longer reduces the number of
  training steps (but never increases it).
Therefore, the batch size that minimizes training time is usually the
largest batch size that still provides a reduction in the number of training
steps required.
- This batch size depends on the dataset, model, and optimizer, and it is
  an open problem how to calculate it other than finding it experimentally
  for every new problem. 🤖
- When comparing batch sizes, beware the distinction between an example
  budget/epoch
  budget (running all experiments while fixing the number of training
  example presentations) and a step budget (running all experiments with
  the number of training steps fixed).
  - Comparing batch sizes with an epoch budget only probes the perfect
    scaling regime, even when larger batch sizes might still provide a
    meaningful speedup by reducing the number of training steps
    required.
- Often, the largest batch size supported by the available hardware will
  be smaller than the critical batch size. Therefore, a good rule of thumb
  (without running any experiments) is to use the largest batch size
  possible.
There is no point in using a larger batch size if it ends up increasing the
training time.

Choosing the batch size to minimize resource consumption

[Click to expand]

There are two types of resource costs associated with increasing the batch
size:
1. Upfront costs, e.g. purchasing new hardware or rewriting the training
  pipeline to implement multi-GPU / multi-TPU training.
2. Usage costs, e.g. billing against the team's resource budgets, billing
  from a cloud provider, electricity / maintenance costs.
If there are significant upfront costs to increasing the batch size, it
might be better to defer increasing the batch size until the project has
matured and it is easier to assess the cost-benefit tradeoff. Implementing
multi-host parallel training programs can introduce
bugs and
subtle issues so it is
probably better to start off with a simpler pipeline anyway. (On the other
hand, a large speedup in training time might be very beneficial early in the
process when a lot of tuning experiments are needed).
We refer to the total usage cost (which may include multiple different kinds
of costs) as the "resource consumption". We can break down the resource
consumption into the following components:

Resource consumption = (resource consumption per step) x (total number of steps)

Increasing the batch size usually allows us to
reduce the total number of steps.
Whether the resource consumption increases or decreases will depend on how
the consumption per step changes.
- Increasing the batch size might decrease the resource consumption. For
  example, if each step with the larger batch size can be run on the same
  hardware as the smaller batch size (with only a small increase in time
  per step), then any increase in the resource consumption per step might
  be outweighed by the decrease in the number of steps.
- Increasing the batch size might not change the resource consumption.
  For example, if doubling the batch size halves the number of steps
  required and doubles the number of GPUs used, the total consumption (in
  terms of GPU-hours) will not change.
- Increasing the batch size might increase the resource consumption. For
  example, if increasing the batch size requires upgraded hardware, the
  increase in consumption per step might outweigh the reduction in the
  number of steps.

Changing the batch size requires re-tuning most hyperparameters

[Click to expand]

The optimal values of most hyperparameters are sensitive to the batch size.
Therefore, changing the batch size typically requires starting the tuning
process all over again.
The hyperparameters that interact most strongly with the batch size, and therefore are most important to tune separately for each batch size, are the optimizer hyperparameters (e.g. learning rate, momentum) and the regularization hyperparameters.
Keep this in mind when choosing the batch size at the start of a project. If
you need to switch to a different batch size later on, it might be
difficult, time consuming, and expensive to re-tune everything for the new
batch size.

How batch norm interacts with the batch size

[Click to expand]

Batch norm is complicated and, in general, should use a different batch size
than the gradient computation to compute statistics. See the
batch norm section for a
detailed discussion.

Choosing the initial configuration

Before beginning hyperparameter tuning we must determine the starting point.
This includes specifying (1) the model configuration (e.g. number of
layers), (2) the optimizer hyperparameters (e.g. learning rate), and (3) the
number of training steps.
Determining this initial configuration will require some manually configured
training runs and trial-and-error.
Our guiding principle is to find a simple, relatively fast, relatively
low-resource-consumption configuration that obtains a "reasonable" result.
- "Simple" means avoiding bells and whistles wherever possible; these can
  always be added later. Even if bells and whistles prove helpful down the
  road, adding them in the initial configuration risks wasting time tuning
  unhelpful features and/or baking in unnecessary complications.
  - For example, start with a constant learning rate before adding fancy
    decay schedules.
- Choosing an initial configuration that is fast and consumes minimal
  resources will make hyperparameter tuning much more efficient.
  - For example, start with a smaller model.
- "Reasonable" performance depends on the problem, but at minimum means
  that the trained model performs much better than random chance on the
  validation set (although it might be bad enough to not be worth
  deploying).
Choosing the number of training steps involves balancing the following
tension:
- On the one hand, training for more steps can improve performance and
  makes hyperparameter tuning easier (see
  Shallue et al. 2018).
- On the other hand, training for fewer steps means that each training run
  is faster and uses fewer resources, boosting tuning efficiency by
  reducing the time between cycles and allowing more experiments to be run
  in parallel. Moreover, if an unnecessarily large step budget is chosen
  initially, it might be hard to change it down the road, e.g. once the
  learning rate schedule is tuned for that number of steps.

A scientific approach to improving model performance

For the purposes of this document, the ultimate goal of machine learning
development is to maximize the utility of the deployed model. Even though many
aspects of the development process differ between applications (e.g. length of
time, available computing resources, type of model), we can typically use the
same basic steps and principles on any problem.

Our guidance below makes the following assumptions:

There is already a fully-running training pipeline along with a
configuration that obtains a reasonable result.
There are enough computational resources available to conduct meaningful
tuning experiments and run at least several training jobs in parallel.

The incremental tuning strategy

Summary: Start with a simple configuration and incrementally make
improvements while building up insight into the problem. Make sure that any
improvement is based on strong evidence to avoid adding unnecessary complexity.

Our ultimate goal is to find a configuration that maximizes the performance
of our model.
- In some cases, our goal will be to maximize how much we can improve the
  model by a fixed deadline (e.g. submitting to a competition).
- In other cases, we want to keep improving the model indefinitely (e.g.
  continually improving a model used in production).
In principle, we could maximize performance by using an algorithm to
automatically search the entire space of possible configurations, but this
is not a practical option.
- The space of possible configurations is extremely large and there are
  not yet any algorithms sophisticated enough to efficiently search this
  space without human guidance.
Most automated search algorithms rely on a hand-designed search space that
defines the set of configurations to search in, and these search spaces can
matter quite a bit.
The most effective way to maximize performance is to start with a simple
configuration and incrementally add features and make improvements while
building up insight into the problem.
- We use automated search algorithms in each round of tuning and
  continually update our search spaces as our understanding grows.
As we explore, we will naturally find better and better configurations and
therefore our "best" model will continually improve.
- We call it a launch when we update our best configuration (which may
  or may not correspond to an actual launch of a production model).
- For each launch, we must make sure that the change is based on strong
  evidence – not just random chance based on a lucky configuration – so
  that we don't add unnecessary complexity to the training pipeline.

At a high level, our incremental tuning strategy involves repeating the
following four steps:

Identify an appropriately-scoped goal for the next round of experiments.
Design and run a set of experiments that makes progress towards this goal.
Learn what we can from the results.
Consider whether to launch the new best configuration.

The remainder of this section will consider this strategy in much greater
detail.

Exploration vs exploitation

Summary: Most of the time, our primary goal is to gain insight into the
problem.

Although one might think we would spend most of our time trying to maximize
performance on the validation set, in practice we spend the majority of our
time trying to gain insight into the problem, and comparatively little time
greedily focused on the validation error.
- In other words, we spend most of our time on "exploration" and only a
  small amount on "exploitation".
In the long run, understanding the problem is critical if we want to
maximize our final performance. Prioritizing insight over short term gains
can help us:
- Avoid launching unnecessary changes that happened to be present in
  well-performing runs merely through historical accident.
- Identify which hyperparameters the validation error is most sensitive
  to, which hyperparameters interact the most and therefore need to be
  re-tuned together, and which hyperparameters are relatively insensitive
  to other changes and can therefore be fixed in future experiments.
- Suggest potential new features to try, such as new regularizers if
  overfitting is an issue.
- Identify features that don't help and therefore can be removed, reducing
  the complexity of future experiments.
- Recognize when improvements from hyperparameter tuning have likely
  saturated.
- Narrow our search spaces around the optimal value to improve tuning
  efficiency.
When we are eventually ready to be greedy, we can focus purely on the
validation error even if the experiments aren't maximally informative about
the structure of the tuning problem.

Choosing the goal for the next round of experiments

Summary: Each round of experiments should have a clear goal and be
sufficiently narrow in scope that the experiments can actually make progress
towards the goal.

Each round of experiments should have a clear goal and be sufficiently
narrow in scope that the experiments can actually make progress towards the
goal: if we try to add multiple features or answer multiple questions at
once, we may not be able to disentangle the separate effects on the results.
Example goals include:
- Try a potential improvement to the pipeline (e.g. a new regularizer,
  preprocessing choice, etc.).
- Understand the impact of a particular model hyperparameter (e.g. the
  activation function)
- Greedily minimize validation error.

Designing the next round of experiments

Summary: Identify which hyperparameters are scientific, nuisance, and
fixed hyperparameters for the experimental goal. Create a sequence of studies to
compare different values of the scientific hyperparameters while optimizing over
the nuisance hyperparameters. Choose the search space of nuisance
hyperparameters to balance resource costs with scientific value.

Identifying scientific, nuisance, and fixed hyperparameters

[Click to expand]

For a given goal, all hyperparameters will be either scientific
hyperparameters, nuisance hyperparameters, or fixed
hyperparameters.
- Scientific hyperparameters are those whose effect on the model's
  performance we're trying to measure.
- Nuisance hyperparameters are those that need to be optimized over in
  order to fairly compare different values of the scientific
  hyperparameters. This is similar to the statistical concept of
  nuisance parameters.
- Fixed hyperparameters will have their values fixed in the current round
  of experiments. These are hyperparameters whose values do not need to
  (or we do not want them to) change when comparing different values of
  the scientific hyperparameters.
  - By fixing certain hyperparameters for a set of experiments, we must
    accept that conclusions derived from the experiments might not be
    valid for other settings of the fixed hyperparameters. In other
    words, fixed hyperparameters create caveats for any conclusions we
    draw from the experiments.
For example, if our goal is to "determine whether a model with more hidden
layers will reduce validation error", then the number of hidden layers is a
scientific hyperparameter.
- The learning rate is a nuisance hyperparameter because we can only
  fairly compare models with different numbers of hidden layers if the
  learning rate is tuned separately for each number of layers (the optimal
  learning rate generally depends on the model architecture).
- The activation function could be a fixed hyperparameter if we have
  determined in prior experiments that the best choice of activation
  function is not sensitive to model depth, or if we are willing to limit
  our conclusions about the number of hidden layers to only cover this
  specific choice of activation function. Alternatively, it could be a
  nuisance parameter if we are prepared to tune it separately for each
  number of hidden layers.
Whether a particular hyperparameter is a scientific hyperparameter, nuisance
hyperparameter, or fixed hyperparameter is not inherent to that
hyperparameter, but changes depending on the experimental goal.
- For example, the choice of activation function could be a scientific
  hyperparameter (is ReLU or tanh a better choice for our problem?), a
  nuisance hyperparameter (is the best 5-layer model better than the best
  6-layer model when we allow several different possible activation
  functions?), or a fixed hyperparameter (for ReLU nets, does adding batch
  normalization in a particular position help?).
When designing a new round of experiments, we first identify the scientific
hyperparameters for our experimental goal.
- At this stage, we consider all other hyperparameters to be nuisance
  hyperparameters.
Next, we convert some of the nuisance hyperparameters into fixed
hyperparameters.
- With limitless resources, we would leave all non-scientific
  hyperparameters as nuisance hyperparameters so that the conclusions we
  draw from our experiments are free from caveats about fixed
  hyperparameter values.
- However, the more nuisance hyperparameters we attempt to tune, the
  greater the risk we fail to tune them sufficiently well for each setting
  of the scientific hyperparameters and end up reaching the wrong
  conclusions from our experiments.
  - As described
    below,
    we could counter this risk by increasing the computational budget,
    but often our maximum resource budget is less than would be needed
    to tune over all non-scientific hyperparameters.
- We choose to convert a nuisance hyperparameter into a fixed
  hyperparameter when, in our judgment, the caveats introduced by fixing
  it are less burdensome than the cost of including it as a nuisance
  hyperparameter.
  - The more a given nuisance hyperparameter interacts with the
    scientific hyperparameters, the more damaging it is to fix its
    value. For example, the best value of the weight decay strength
    typically depends on the model size, so comparing different model
    sizes assuming a single specific value of the weight decay would not
    be very insightful.
Although the type we assign to each hyperparameter depends on the
experimental goal, we have the following rules of thumb for certain
categories of hyperparameters:
- Of the various optimizer hyperparameters (e.g. the learning rate,
  momentum, learning rate schedule parameters, Adam betas etc.), at least
  some of them will be nuisance hyperparameters because they tend to
  interact the most with other changes.
  - They are rarely scientific hyperparameters because a goal like "what
    is the best learning rate for the current pipeline?" doesn't give
    much insight – the best setting could easily change with the next
    pipeline change anyway.
  - Although we might fix some of them occasionally due to resource
    constraints or when we have particularly strong evidence that they
    don't interact with the scientific parameters, we should generally
    assume that optimizer hyperparameters must be tuned separately to
    make fair comparisons between different settings of the scientific
    hyperparameters, and thus shouldn't be fixed.
    - Furthermore, we have no a priori reason to prefer one
      optimizer hyperparameter value over another (e.g. they don't
      usually affect the computational cost of forward passes or
      gradients in any way).
- In contrast, the choice of optimizer is typically a scientific
  hyperparameter or fixed hyperparameter.
  - It is a scientific hyperparameter if our experimental goal involves
    making fair comparisons between two or more different optimizers
    (e.g. "determine which optimizer produces the lowest validation
    error in a given number of steps").
  - Alternatively, we might make it a fixed hyperparameter for a variety
    of reasons, including (1) prior experiments make us believe that the
    best optimizer for our problem is not sensitive to current
    scientific hyperparameters; and/or (2) we prefer to compare values
    of the scientific hyperparameters using this optimizer because its
    training curves are easier to reason about; and/or (3) we prefer to
    use this optimizer because it uses less memory than the
    alternatives.
- Hyperparameters introduced by a regularization technique are typically
  nuisance hyperparameters, but whether or not we include the
  regularization technique at all is a scientific or fixed hyperparameter.
  - For example, dropout adds code complexity, so when deciding whether
    to include it we would make "no dropout" vs "dropout" a scientific
    hyperparameter and the dropout rate a nuisance hyperparameter.
    - If we decide to add dropout to our pipeline based on this
      experiment, then the dropout rate would be a nuisance
      hyperparameter in future experiments.
- Architectural hyperparameters are often scientific or fixed
  hyperparameters because architecture changes can affect serving and
  training costs, latency, and memory requirements.
  - For example, the number of layers is typically a scientific or fixed
    hyperparameter since it tends to have dramatic consequences for
    training speed and memory usage.
In some cases, the sets of nuisance and fixed hyperparameters will depend on
the values of the scientific hyperparameters.
- For example, suppose we are trying to determine which optimizer out of
  Nesterov momentum and Adam results in the lowest validation error. The
  scientific hyperparameter is the optimizer, which takes values
  {"Nesterov_momentum", "Adam"}. The value
  optimizer="Nesterov_momentum" introduces the nuisance/fixed
  hyperparameters {learning_rate, momentum}, but the value
  optimizer="Adam" introduces the nuisance/fixed hyperparameters
  {learning_rate, beta1, beta2, epsilon}.
- Hyperparameters that are only present for certain values of the
  scientific hyperparameters are called conditional hyperparameters.
- We should not assume two conditional hyperparameters are the same just
  because they have the same name! In the above example, the conditional
  hyperparameter called learning_rate is a different hyperparameter
  for optimizer="Nesterov_momentum" versus optimizer="Adam". Its role
  is similar (although not identical) in the two algorithms, but the range
  of values that work well in each of the optimizers is typically
  different by several orders of magnitude.

Creating a set of studies

[Click to expand]

Once we have identified the scientific and nuisance hyperparameters, we
design a "study" or sequence of studies to make progress towards the
experimental goal.
- A study specifies a set of hyperparameter configurations to be run for
  subsequent analysis. Each configuration is called a "trial".
- Creating a study typically involves choosing the hyperparameters that
  will vary across trials, choosing what values those hyperparameters can
  take on (the "search space"), choosing the number of trials, and
  choosing an automated search algorithm to sample that many trials from
  the search space. Alternatively, we could create a study by specifying
  the set of hyperparameter configurations manually.
The purpose of the studies is to run the pipeline with different values of
the scientific hyperparameters, while at the same time "optimizing away"
(or "optimizing over") the nuisance hyperparameters so that comparisons
between different values of the scientific hyperparameters are as fair as
possible.
In the simplest case, we would make a separate study for each configuration
of the scientific parameters, where each study tunes over the nuisance
hyperparameters.
- For example, if our goal is to select the best optimizer out of Nesterov
  momentum and Adam, we could create one study in which
  optimizer="Nesterov_momentum" and the nuisance hyperparameters are
  {learning_rate, momentum}, and another study in which
  optimizer="Adam" and the nuisance hyperparameters are {learning_rate, beta1, beta2, epsilon}. We would compare the two optimizers by
  selecting the best performing trial from each study.
- We can use any gradient-free optimization algorithm, including methods
  such as Bayesian optimization or evolutionary algorithms, to optimize
  over the nuisance hyperparameters, although
  we prefer
  to use quasi-random search in the
  exploration phase of tuning because of a
  variety of advantages it has in this setting.
  After exploration concludes, if
  state-of-the-art Bayesian optimization software is available, that is
  our preferred choice.
In the more complicated case where we want to compare a large number of
values of the scientific hyperparameters and it is impractical to make that
many independent studies, we can include the scientific parameters in the
same search space as the nuisance hyperparameters and use a search algorithm
to sample values of both the scientific and nuisance hyperparameters in a
single study.
- When taking this approach, conditional hyperparameters can cause
  problems since it is hard to specify a search space unless the set of
  nuisance hyperparameters is the same for all values of the scientific
  hyperparameters.
- In this case,
  our preference
  for using quasi-random search over fancier black-box optimization tools
  is even stronger, since it ensures that we obtain a relatively uniform
  sampling of values of the scientific hyperparameters. Regardless of the
  search algorithm, we need to make sure somehow that it searches the
  scientific parameters uniformly.

Striking a balance between informative and affordable experiments

[Click to expand]

When designing a study or sequence of studies, we need to allocate a limited
budget in order to adequately achieve the following three desiderata:
1. Comparing enough different values of the scientific hyperparameters.
2. Tuning the nuisance hyperparameters over a large enough search space.
3. Sampling the search space of nuisance hyperparameters densely enough.
The better we can achieve these three desiderata, the more insight we can
extract from our experiment.
- Comparing as many values of the scientific hyperparameters as possible
  broadens the scope of the insights we gain from the experiment.
- Including as many nuisance hyperparameters as possible and allowing each
  nuisance hyperparameter to vary over as wide a range as possible
  increases our confidence that a "good" value of the nuisance
  hyperparameters exists in the search space for each configuration of
  the scientific hyperparameters.
  - Otherwise, we might make unfair comparisons between values of the
    scientific hyperparameters by not searching possible regions of the
    nuisance parameter space where better values might lie for some
    values of the scientific parameters.
- Sampling the search space of nuisance hyperparameters as densely as
  possible increases our confidence that any good settings for the
  nuisance hyperparameters that happen to exist in our search space will
  be found by the search procedure.
  - Otherwise, we might make unfair comparisons between values of the
    scientific parameters due to some values getting luckier with the
    sampling of the nuisance hyperparameters.
Unfortunately, improvements in any of these three dimensions require
either increasing the number of trials, and therefore increasing the
resource cost, or finding a way to save resources in one of the other
dimensions.
- Every problem has its own idiosyncrasies and computational constraints,
  so how to allocate resources across these three desiderata requires some
  level of domain knowledge.
- After running a study, we always try to get a sense of whether the study
  tuned the nuisance hyperparameters well enough (i.e. searched a large
  enough space extensively enough) to fairly compare the scientific
  hyperparameters (as described in greater detail
  below).

Extracting insight from experimental results

Summary: In addition to trying to achieve the original scientific goal of
each group of experiments, go through a checklist of additional questions and,
if issues are discovered, revise the experiments and rerun them.

Ultimately, each group of experiments has a specific goal and we want to
evaluate the evidence the experiments provide toward that goal.
- However, if we ask the right questions, we will often find issues that
  need to be corrected before a given set of experiments can make much
  progress towards their original goal.
  - If we don’t ask these questions, we may draw incorrect conclusions.
- Since running experiments can be expensive, we also want to take the
  opportunity to extract other useful insights from each group of
  experiments, even if these insights are not immediately relevant to the
  current goal.
Before analyzing a given set of experiments to make progress toward their
original goal, we should ask ourselves the following additional questions:
- Is the search space large enough?
  - If the optimal point from a study is near the boundary of the search
    space in one or more dimensions, the search is probably not wide
    enough. In this case, we should run another study with an expanded
    search space.
- Have we sampled enough points from the search space?
  - If not, run more points or be less ambitious in the tuning goals.
- What fraction of the trials in each study are infeasible (i.e.
  trials that diverge, get really bad loss values, or fail to run at all
  because they violate some implicit constraint)?
  - When a very large fraction of points in a study are infeasible
    we should try to adjust the search space to avoid sampling such
    points, which sometimes requires reparameterizing the search space.
  - In some cases, a large number of infeasible points can indicate a
    bug in the training code.
- Does the model exhibit optimization issues?
- What can we learn from the training curves of the best trials?
  - For example, do the best trials have training curves consistent with
    problematic overfitting?
If necessary, based on the answers to the questions above, refine the most
recent study (or group of studies) to improve the search space and/or sample
more trials, or take some other corrective action.
Once we have answered the above questions, we can move on to evaluating the
evidence the experiments provide towards our original goal (for example,
evaluating whether a change is useful).

Identifying bad search space boundaries

[Click to expand]

A search space is suspicious if the best point sampled from it is close to
its boundary. We might find an even better point if we expanded the search
range in that direction.
To check search space boundaries, we like to plot completed trials on what
we call basic hyperparameter axis plots where we plot the validation
objective value versus one of the hyperparameters (e.g. learning rate). Each
point on the plot corresponds to a single trial.
- The validation objective value for each trial should usually be the best
  value it achieved over the course of training.

Example of bad search space boundaries Example of good search space boundaries

Figure 1: Examples of bad search space boundaries and acceptable search space boundaries.

The plots in Figure 1 show the error rate (lower is better)
against the initial learning rate.
If the best points cluster towards the edge of a search space (in some
dimension), then the search space boundaries might need to be expanded until
the best observed point is no longer close to the boundary.
Often, a study will include "infeasible" trials that diverge or get very bad
results (marked with red Xs in the above plots).
- If all trials are infeasible for learning rates greater than some
  threshold value, and if the best performing trials have learning rates
  at the edge of that region, the model may suffer from stability issues
  preventing it from accessing higher learning
  rates.

Not sampling enough points in the search space

[Click to expand]

In general,
it can be very difficult to know
if the search space has been sampled densely enough. 🤖
Running more trials is of course better, but comes at an obvious cost.
Since it is so hard to know when we have sampled enough, we usually sample
what we can afford and try to calibrate our intuitive confidence from
repeatedly looking at various hyperparameter axis plots and trying to get a
sense of how many points are in the "good" region of the search space.

Examining the training curves

[Click to expand]

Summary: Examining the training curves is an easy way to identify common
failure modes and can help us prioritize what actions to take next.

Although in many cases the primary objective of our experiments only
requires considering the validation error of each trial, we must be careful
when reducing each trial to a single number because it can hide important
details about what’s going on below the surface.
For every study, we always look at the training curves (training error
and validation error plotted versus training step over the duration of
training) of at least the best few trials.
Even if this is not necessary for addressing the primary experimental
objective, examining the training curves is an easy way to identify common
failure modes and can help us prioritize what actions to take next.
When examining the training curves, we are interested in the following
questions.
Are any of the trials exhibiting problematic overfitting?
- Problematic overfitting occurs when the validation error starts
  increasing at some point during training.
- In experimental settings where we optimize away nuisance hyperparameters
  by selecting the "best" trial for each setting of the scientific
  hyperparameters, we should check for problematic overfitting in at
  least each of the best trials corresponding to the settings of the
  scientific hyperparameters that we’re comparing.
  - If any of the best trials exhibits problematic overfitting, we
    usually want to re-run the experiment with additional regularization
    techniques and/or better tune the existing regularization parameters
    before comparing the values of the scientific hyperparameters.
    - This may not apply if the scientific hyperparameters include
      regularization parameters, since then it would not be surprising
      if low-strength settings of those regularization parameters
      resulted in problematic overfitting.
  - Reducing overfitting is often straightforward using common
    regularization techniques that add minimal code complexity or extra
    computation (e.g. dropout, label smoothing, weight decay), so it’s
    usually no big deal to add one or more of these to the next round of
    experiments.
  - For example, if the scientific hyperparameter is "number of hidden
    layers" and the best trial that uses the largest number of hidden
    layers exhibited problematic overfitting, then we would usually
    prefer to try it again with additional regularization instead of
    immediately selecting the smaller number of hidden layers.
  - Even if none of the "best" trials are exhibiting problematic
    overfitting, there might still be a problem if it occurs in any of
    the trials.
    - Selecting the best trial suppresses configurations exhibiting
      problematic overfitting and favors those that do not. In other
      words, it will favor configurations with more regularization.
    - However, anything that makes training worse can act as a
      regularizer, even if it wasn't intended that way. For example,
      choosing a smaller learning rate can regularize training by
      hobbling the optimization process, but we typically don't want
      to choose the learning rate this way.
    - So we must be aware that the "best" trial for each setting of
      the scientific hyperparameters might be selected in such a way
      that favors "bad" values of some of the scientific or nuisance
      hyperparameters.
Is there high step-to-step variance in the training or validation error late
in training?
- If so, this could interfere with our ability to compare different values
  of the scientific hyperparameters (since each trial randomly ends on a
  "lucky" or "unlucky" step) and our ability to reproduce the result of
  the best trial in production (since the production model might not end
  on the same "lucky" step as in the study).
- The most likely causes of step-to-step variance are batch variance (from
  randomly sampling examples from the training set for each batch), small
  validation sets, and using a learning rate that’s too high late in
  training.
- Possible remedies include increasing the batch size, obtaining more
  validation data, using learning rate decay, or using Polyak averaging.
Are the trials still improving at the end of training?
- If so, this indicates that we are in the
  "compute bound" regime
  and we may benefit from
  increasing the number of training steps
  or changing the learning rate schedule.
Has performance on the training and validation sets saturated long before
the final training step?
- If so, this indicates that we are in the
  "not compute-bound"
  regime and that we may be able to
  decrease the number of training steps.
Although we cannot enumerate them all, there are many other additional
behaviors that can become evident from examining the training curves (e.g.
training loss increasing during training usually indicates a bug in the
training pipeline).

Detecting whether a change is useful with isolation plots

[Click to expand]

Isolation plot that investigates the best value of weight decay for ResNet-50
trained on ImageNet.

Figure 2: Isolation plot that investigates the best value of weight decay for ResNet-50 trained on ImageNet.

Often, the goal of a set of experiments is to compare different values of a
scientific hyperparameter.
- For example, we may want to determine the value of weight decay that
  results in the best validation error.
An isolation plot is a special case of the basic hyperparameter axis
plot. Each point on an isolation plot corresponds to the performance of the
best trial across some (or all) of the nuisance hyperparameters.
- In other words, we plot the model performance after "optimizing away"
  the nuisance hyperparameters.
An isolation plot makes it easier to perform an apples-to-apples comparison
between different values of the scientific hyperparameter.
For example, Figure 2 reveals the value of weight decay that
produces the best validation performance for a particular configuration of
ResNet-50 trained on ImageNet.
- If our goal is to determine whether to include weight decay at all, then
  we would compare the best point from this plot against the baseline of
  no weight decay. For a fair comparison, the baseline should also have
  its learning rate equally well tuned.
When we have data generated by (quasi)random search and are considering a
continuous hyperparameter for an isolation plot, we can approximate the
isolation plot by bucketing the x-axis values of the basic hyperparameter
axis plot and taking the best trial in each vertical slice defined by the
buckets.

Automate generically useful plots

[Click to expand]

The more effort it is to generate plots, the less likely we are to look at
them as much as we should, so it behooves us to set up our infrastructure to
automatically produce as many of them as possible.
At a minimum, we automatically generate basic hyperparameter axis plots for
all hyperparameters that we vary in an experiment.
Additionally, we automatically produce training curves for all trials and
make it as easy as possible to find the best few trials of each study and
examine their training curves.
There are many other potential plots and visualizations we can add that can
be useful. Although the ones described above are a good starting point, to
paraphrase Geoffrey Hinton, "Every time you plot something new, you learn
something new."

Determining whether to adopt a training pipeline change or hyperparameter configuration

Summary: When deciding whether to make a change to our model or training
procedure or adopt a new hyperparameter configuration going forward, we need to
be aware of the different sources of variation in our results.

When we are trying to improve our model, we might observe that a particular
candidate change initially achieves a better validation error compared to
our incumbent configuration, but find that after repeating the experiment
there is no consistent advantage. Informally, we can group the most
important sources of variation that might cause such an inconsistent result
into the following broad categories:
- Training procedure variance, retrain variance, or trial
  variance: the variation we see between training runs that use the same
  hyperparameters, but different random seeds.
  - For example, different random initializations, training data
    shuffles, dropout masks, patterns of data augmentation operations,
    and orderings of parallel arithmetic operations, are all potential
    sources of trial variance.
- Hyperparameter search variance, or study variance: the variation
  in results caused by our procedure to select the hyperparameters.
  - For example, we might run the same experiment with a particular
    search space, but with two different seeds for quasi-random search
    and end up selecting different hyperparameter values.
- Data collection and sampling variance: the variance from any sort of
  random split into training, validation, and test data or variance due to
  the training data generation process more generally.
It is all well and good to make comparisons of validation error rates
estimated on a finite validation set using fastidious statistical tests, but
often the trial variance alone can produce statistically significant
differences between two different trained models that use the same
hyperparameter settings.
We are most concerned about study variance when trying to make conclusions
that go beyond the level of an individual point in hyperparameters space.
- The study variance depends on the number of trials and the search space
  and we have seen cases where it is larger than the trial variance as
  well as cases where it is much smaller.
Therefore, before adopting a candidate change, consider running the best
trial N times to characterize the run-to-run trial variance.
- Usually, we can get away with only recharacterizing the trial variance
  after major changes to the pipeline, but in some applications we might
  need fresher estimates.
- In other applications, characterizing the trial variance is too costly
  to be worth it.
At the end of the day, although we only want to adopt changes (including new
hyperparameter configurations) that produce real improvements, demanding
complete certainty that something helps isn't the right answer either.
Therefore, if a new hyperparameter point (or other change) gets a better
result than the baseline (taking into account the retrain variance of both
the new point and the baseline as best we can), then we probably should
adopt it as the new baseline for future comparisons.
- However, we should only adopt changes that produce improvements that
  outweigh any complexity they add.

After exploration concludes

Summary: Bayesian optimization tools are a compelling option once we’re
done exploring for good search spaces and have decided what hyperparameters even
should be tuned at all.

At some point, our priorities will shift from learning more about the tuning
problem to producing a single best configuration to launch or otherwise use.
At this point, there should be a refined search space that comfortably
contains the local region around the best observed trial and has been
adequately sampled.
Our exploration work should have revealed the most essential hyperparameters
to tune (as well as sensible ranges for them) that we can use to construct a
search space for a final automated tuning study using as large a tuning
budget as possible.
Since we no longer care about maximizing our insight into the tuning
problem, many of
the advantages of quasi-random search
no longer apply and Bayesian optimization tools should be used to
automatically find the best hyperparameter configuration.
- Open-Source Vizier implements
  a variety of sophisticated algorithms for tuning ML models, including
  Bayesian Optimization algorithms.
- If the search space contains a non-trivial volume of divergent points
  (points that get NaN training loss or even training loss many standard
  deviations worse than the mean), it is important to use black box
  optimization tools that properly handle trials that diverge (see
  Bayesian Optimization with Unknown Constraints
  for an excellent way to deal with this issue). Open-Source Vizier
  has support for divergent points by marking trials as infeasible, although it may not use our preferred approach from Gelbart et al., depending on how it is configured.
At this point, we should also consider checking the performance on the test
set.
- In principle, we could even fold the validation set into the training
  set and retraining the best configuration found with Bayesian
  optimization. However, this is only appropriate if there won't be future
  launches with this specific workload (e.g. a one-time Kaggle
  competition).

Determining the number of steps for each training run

There are two types of workloads: those that are compute-bound and those
that are not.
When training is compute-bound, training is limited by how long we are
willing to wait and not by how much training data we have or some other
factor.
- In this case, if we can somehow train longer or more efficiently, we
  should see a lower training loss and, with proper tuning, an improved
  validation loss.
- In other words, speeding up training is equivalent to improving
  training and the "optimal" training time is always "as long as we can
  afford."
- That said, just because a workload is compute-limited doesn't mean
  training longer/faster is the only way to improve results.
When training is not compute-bound, we can afford to train as long as we
would like to, and, at some point, training longer doesn't help much (or
even causes problematic overfitting).
- In this case, we should expect to be able to train to very low training
  loss, to the point where training longer might slightly reduce the
  training loss, but will not meaningfully reduce the validation loss.
- Particularly when training is not compute-bound, a more generous
  training time budget can make tuning easier, especially when tuning
  learning rate decay schedules, since they have a particularly strong
  interaction with the training budget.
  - In other words, very stingy training time budgets might require a
    learning rate decay schedule tuned to perfection in order to achieve
    a good error rate.
Regardless of whether a given workload is compute-bound or not, methods that
increase the variance of the gradients (across batches) will usually result
in slower training progress, and thus may increase the number of training
steps required to reach a particular validation loss. High gradient variance
can be caused by:
- Using a smaller batch size
- Adding data augmentation
- Adding some types of regularization (e.g. dropout)

Deciding how long to train when training is not compute-bound

Our main goal is to ensure we are training long enough for the model to
reach the best possible result, while avoiding being overly wasteful in the
number of training steps.
When in doubt, err on the side of training longer. Performance should never
degrade when training longer, assuming retrospective (optimal) checkpoint
selection is used properly and checkpoints are frequent enough.
Never tune the max_train_steps number in a study. Pick a value and use it
for all trials. From these trials, plot the training step that retrospective
checkpoint selection finds in order to refine the choice of
max_train_steps.
- For example, if the best step is always during the first 10% of
  training, then the maximum number of steps is way too high.
- Alternatively, if the best step is consistently in the last 25% of
  training we might benefit from training longer and re-tuning the decay
  schedule.
The ideal number of training steps can change when the architecture or data
changes (e.g. adding data augmentation).
Below we describe how to pick an initial candidate value for
max_train_steps based on the number of steps necessary to "perfectly fit"
the training set using a constant learning rate.
- Note, we are not using the phrase "perfectly fit the training set" in a
  precise or mathematically well-defined way. It is merely meant as an
  informal descriptor to indicate a very low training loss.
  - For example, when training with the log loss, absent regularization
    terms, we might see the training loss keep slowly improving until we
    reach floating point limits as the network weights grow without
    bound and the predictions of the model on the training set become
    increasingly confident. In this case, we might say the model
    "perfectly fit" the training set around the time the
    misclassification error reached zero on the training set.
- The starting value for max_train_steps we find may need to be
  increased if the amount of gradient noise in the training procedure
  increases.
  - For example, if data augmentation or regularizers like dropout are
    introduced to the model.
- It may be possible to decrease max_train_steps if the training process
  improves somehow.
  - For example, with a better tuned optimizer or a better tuned
    learning rate schedule.

Algorithm for picking an initial candidate for max_train_steps using a learning rate sweep

[Click to expand]

This procedure assumes it is possible to not only "perfectly" fit the
training set, but to do so using a constant learning rate schedule.
If it is possible to perfectly fit the entire training set, then there must
exist a configuration (with some value of max_train_steps) that perfectly
fits the training set; find any such configuration and use its value of
max_train_steps as a starting point N.
Run a constant learning rate sweep (i.e. grid search the learning rate)
without data augmentation and without regularization where each trial trains
for N steps.
The number of steps required for the fastest trial in the sweep to reach
perfect training performance is our initial guess for max_train_steps.
NOTE: Bad search spaces can make it possible to engage in
self-deception.
- For example, if all the learning rates in a study are too small, we
  might incorrectly conclude that a very large value of max_train_steps
  is necessary.
- At a minimum, we should check that the optimal learning rate in the
  study is not at the boundary of the search space.

Deciding how long to train when training is compute-bound

In some cases, training loss keeps improving indefinitely and our patience
and computational resources become the limiting factors.
If training loss (or even validation loss) keeps improving indefinitely,
should we always train as long as we can afford? Not necessarily.
- We might be able to tune more effectively by running a larger number of
  shorter experiments and reserving the longest "production length" runs
  for the models we hope to launch.
- As the training time for trials approaches our patience limit, tuning
  experiments become more relevant for our potential launch candidates,
  but we can complete fewer of them.
- There are probably many questions we can answer while only training for
  ~10% of the production length, but there is always a risk that our
  conclusions at this time limit will not apply to experiments at 20% of
  the production length, let alone 100%.
Tuning in multiple rounds with increasing, per-trial training step limits is
a sensible approach.
- We can do as many rounds as we want, but usually 1-3 are the most
  practical.
- Essentially, try to obtain as much understanding of the problem as
  possible using trials with a very quick turnaround time, trading off
  tuning thoroughness with relevance to the final, longest runs.
- Once a given per-trial time limit has generated useful insights, we can
  increase the training time and continue tuning, double-checking our
  conclusions from the shorter runs as needed.
As a starting point, we recommend two rounds of tuning:
- Round 1: Shorter runs to find good model and optimizer hyperparameters.
- Round 2: Very few long runs on good hyperparameter points to get the
  final model.
The biggest question going from Round i → Round i+1 is how to
adjust learning rate decay schedules.
- One common pitfall when adjusting learning rate schedules between rounds
  is using all the extra training steps with too small of a learning rate.

Round 1

[Click to expand]

Unfortunately, there is no guarantee that good hyperparameters found in
short, incomplete training are still good choices when training length is
significantly increased. However, for some kinds of hyperparameters, they
are often correlated enough for Round 1 to be useful.
What hyperparameter values found in shorter runs do we expect to transfer to
longer training runs? For all of this, we need more research. But based on
what we know so far, here are the authors’ suspicions in order of decreasing
probability of transferring:
- Very likely to transfer
  - Early training instability can be resolved in the first round of
    tuning using a smaller number of training steps. Perhaps these
    hyperparameters are the closest thing to a sure bet for transfer
    that we have.
    - Warmup length
    - Initialization
- Likely to transfer
  - Model architecture - A dramatic win in the model architecture will
    usually transfer, but there are probably many counterexamples.
- Might transfer
  - Optimization algorithm/optimizer hyperparameters - We think this
    would "loosely" transfer. It’s definitely weaker than the things
    above it.
  - Data augmentation
  - Regularization
    - If it isn't possible to perfectly fit the training set, the
      model might be in a regime where regularization is unlikely to
      help very much.
- Unlikely to transfer
  - Learning rate schedule: unlikely to transfer perfectly.
    - This paper suggests that
      even decay schedule transfers, but we don't believe this is true
      in general. Example: Tuning sqrt decay on small # of training
      steps then extending to large # will result in the majority of
      training occurring at overly small steps.
      - One can likely do "good enough" with most schedules in the
        limit of extreme training budget, but noticeable performance
        improvements can likely be seen if it is tuned.
    - Understanding Short-Horizon Bias in Stochastic
      Meta-Optimization describes
      the dangers of trying to pick learning rates myopically.

Round 2

[Click to expand]

Run the best hyperparameter configuration from Round 1.
(Speculation) 🤖 Use the extra steps to extend the period of training at
a high learning rate.
- E.g. if linear schedule then keep the length of the decay fixed from
  Round 1 and extend the period of constant lr in the beginning.
- For cosine decay, just keep the base lr from Round 1 and extend
  max_train_steps as in
  Chinchilla paper.
More rounds might make sense for teams with very mature modeling and tuning
pipelines and very long and expensive production training runs, but they
will often be overkill.
- We've described how to transfer from Step 1 → Step 2. If we didn't care
  about analysis time and if making efficient use of compute was the
  overriding concern, then the ideal would be to exponentially increase
  the length of training runs (and thus the end-to-end time to complete a
  study) over many different rounds of tuning.
  - At each round we systematically ensure our choices continue to hold
    up.
  - New ideas go through a pipeline that progressively derisks them
    using increasingly long-running experiments from Step i to Step i+1.

Additional guidance for the training pipeline

Optimizing the input pipeline

Summary: The causes and interventions of input-bound pipelines are highly
task-dependent; use a profiler and look out for common issues.

Use an appropriate profiler to diagnose input-bound pipelines. For example,
Perfetto for JAX or
TensorFlow profiler for
TensorFlow.
Ultimately, the specific causes and interventions will be highly
task-dependent. Broader engineering considerations (e.g. minimizing disk
footprint) may warrant worse input pipeline performance.
Common causes:
- Data are not colocated with the training process, causing I/O latency
  (this might happen when reading training data over a network).
- Expensive online data preprocessing (consider doing this once offline
  and saving).
- Unintentional synchronization barriers that interfere with data pipeline
  prefetching. For example, when synchronizing metrics between the device
  and host in CommonLoopUtils
  (link).
Common tips:
- Instrument input pipeline to prefetch examples (e.g.
  tf.data.Dataset.prefetch)
- Remove unused features/metadata from each as early in the pipeline as
  possible.
- Increase the replication of the number of jobs generating examples for
  the input pipeline. For example, by using the
  tf.data service.

Evaluating model performance

Summary: Run evaluation at larger batch sizes than training. Run
evaluations at regular step intervals, not regular time intervals.

Evaluation settings

[Click to expand]

There are several settings in which we can evaluate the performance of our
models.
- Online evaluation - metrics are collected when the model is serving
  predictions in a production environment.
- Offline evaluation - metrics are collected when the model is run on
  offline train/validation/test sets that are representative of the
  production environment.
- Periodic evaluations - metrics are collected during model training
  that might either be a proxy for the offline evaluation, and/or on a
  subset of the data used in offline evaluation.
Online evaluation is the gold standard, but is often impractical during the
model development phase.
Depending on the problem, offline evaluation can be fairly involved and
computationally expensive.
Periodic evaluations are the most practical and economical choice, but may
not fully represent the production environment.
- Our goal during periodic evaluation is to use an expedient proxy of the
  offline evaluation, without sacrificing the reliability of the signal we
  get during training.

Setting up periodic evaluations

[Click to expand]

We run periodic evaluations during training to monitor its progress in real
time, to
facilitate retrospective model checkpoint selection,
and so that we can
examine the training curves at the end of training.
The simplest configuration is to perform both training and periodic
evaluations within the same compute instance, periodically alternating
between training and evaluation.
- In this case, the batch size used to perform evaluations should be at
  least as large as the batch size used for training because model
  activations don't need to be maintained during evaluation, lowering the
  computational requirements per example.
Periodic evaluations should be done at regular step intervals, not time
intervals.
- Evaluating based on time intervals can make it harder to interpret the
  training curves, especially when training may suffer from preemptions of
  the training jobs, network latency issues, etc.
Periodicity in valid/test metrics (when using a shuffled
train/validation/test split) can indicate implementation bugs such as test
data having overlap with training data, or training data not being properly
shuffled. Evaluating at regular step intervals can make these issues easier
to catch.
Partial batches can occur when the evaluation sets are not divisible by the
batch size. Ensure that the padded examples are correctly weighted to prevent
the loss function from being biased by them. Often, these padded examples
can be given a weight of zero.
Save sufficient information per evaluation to support offline analysis.
Ideally, we would save predictions on a selection of individual examples
since they can be invaluable for debugging.
- Generating artifacts like
  SavedModels make it easy
  to do ad-hoc model inspection after evaluation jobs finish.

Choosing a sample for periodic evaluation

[Click to expand]

The periodic evaluation job might not run fast enough to compute metrics on
the full offline evaluation set in a reasonable amount of time. This often
necessitates sampling data for periodic evaluation.
We consider the following factors when constructing a sampled dataset:
- Sample size
  - Check that the performance computed on the sampled dataset used by
    the periodic job matches the performance on the whole offline
    evaluation set, i.e. there is no skew between the sampled set and
    the full dataset.
  - The dataset used for periodic evaluation should be small enough that
    it’s easy to generate model predictions over its entirety, but large
    enough that improvements to the model can be accurately measured
    (i.e. not overwhelmed by label noise).
  - It should be large enough to accommodate multiple such evaluations
    across trials in sequence, and still produce accurate estimates.
    That is, to avoid adaptively "fitting" to the validation set over
    time, in a way that doesn't generalize to a held-out test set.
    However, this consideration is rarely a practical concern.
- Imbalanced datasets
  - For imbalanced datasets, performance on rare classes of examples
    will often be noisy.
  - For datasets with a small number of examples in a class label, log
    the number of examples predicted correctly to get more insight into
    accuracy improvements (.05 sensitivity improvement sounds exciting,
    but was it just one more example correct?).

Saving checkpoints and retrospectively selecting the best checkpoint

Summary: Run training for a fixed number of steps and retrospectively
choose the best checkpoint from the run.

Most deep learning frameworks support
model checkpointing.
That is, the current state of the model is periodically preserved on disk.
This allows the training job to be resilient to compute instance
interruptions.
The best checkpoint is often not the last checkpoint, particularly when the
validation set performance does not continue to increase over time but
rather fluctuates about a particular value.
Set up the pipeline to keep track of the N best checkpoints seen so far
during training. At the end of training, model selection is then a matter of
choosing the best checkpoint seen during training. We call this
retrospective optimal checkpoint selection.
Supporting prospective early stopping is usually not necessary, since we’re
pre-specifying a trial budget and are preserving the N best checkpoints seen
so far.

Setting up experiment tracking

Summary: When tracking different experiments, make sure to note a number
of essentials like the best performance of a checkpoint in the study, and a
short description of the study.

We've found that keeping track of experiment results in a spreadsheet has
been helpful for the sorts of modeling problems we've worked on. It often
has the following columns:
- Study name
- A link to wherever the config for the study is stored.
- Notes or a short description of the study.
- Number of trials run
- Performance on the validation set of the best checkpoint in the study.
- Specific reproduction commands or notes on what unsubmitted changes were
  necessary to launch training.
Find a tracking system that captures at least the information listed above
and is convenient for the people doing it. Untracked experiments might as
well not exist.

Batch normalization implementation details

Summary: Nowadays batch norm can often be replaced with LayerNorm, but in
cases where it cannot, there are tricky details when changing the batch size or
number of hosts.

Batch norm normalizes activations using their mean and variance over the
current batch, but in the multi-device setting these statistics are
different on each device unless explicitly synchronized.
Anecdotal reports (mostly on ImageNet) say calculating these normalizing
statistics using only ~64 examples actually works better in practice (see
Ghost Batch Norm from this paper).
Decoupling the total batch size and the number of examples used to calculate
batch norm statistics is particularly useful for batch size comparisons.
Ghost batch norm implementations do not always correctly handle the case
where the per-device batch size > virtual batch size. In this case we'd
actually need to subsample the batch on each device in order to get the
proper number of batch norm statistic examples.
Exponential moving averages used in test mode batch norm are just a linear
combination of training statistics, so these EMAs only need to be
synchronized before saving them in checkpoints. However, some common
implementations of batch norm do not synchronize these EMAs and only save
the EMA from the first device.

Considerations for multi-host pipelines

Summary: for logging, evals, RNGs, checkpointing, and data sharding,
multi-host training can make it very easy to introduce bugs!

Ensure the pipeline is only logging and checkpointing on one host.
Make sure before evaluation or checkpointing is run, the batch norm
statistics are synchronized across hosts.
It is critical to have RNG seeds that are the same across hosts (for model
initialization), and seeds that are different across hosts (for data
shuffling/preprocessing), so make sure to mark them appropriately.
Sharding data files across hosts is usually recommended for improved
performance.

FAQs

What is the best learning rate decay schedule family?

[Click to expand]

It’s an open problem. It’s not clear how to construct a set of rigorous
experiments to confidently answer what the "best" LR decay schedule is.
Although we don't know the best schedule family, we're confident that it’s
important to have some (non-constant) schedule and that tuning it matters.
Different learning rates work best at different times during the
optimization process. Having some sort of schedule makes it more likely for
the model to hit a good learning rate.

Which learning rate decay should I use as a default?

[Click to expand]

Our preference is either linear decay or cosine decay, and a bunch of other
schedule families are probably good too.

Why do some papers have complicated learning rate schedules?

[Click to expand]

It’s not uncommon to see papers with complicated piecewise learning rate
(LR) decay schedules.
Readers often wonder how the authors arrived at such a complicated schedule.
Many complicated LR decay schedules are the result of tuning the schedule as
a function of the validation set performance in an ad hoc way:
1. Start a single training run with some simple LR decay (or a constant
  learning rate).
2. Keep training running until the performance seems to stagnate. If this
  happens, pause training. Resume it with a perhaps steeper LR decay
  schedule (or smaller constant learning rate) from this point. Repeat
  this process until the conference/launch deadline.
Blithely copying the resulting schedule is generally not a good idea since
the best particular schedule will be sensitive to a host of other
hyperparameter choices.
- Better to copy the algorithm that produced the schedule, although this
  is rarely possible when arbitrary human judgment produced the schedule.
This type of validation-error-sensitive schedule is fine to use if it can be
fully automated, but human-in-the-loop schedules that are a function of
validation error are brittle and not easily reproducible, so we recommend
avoiding them.
- Before publishing results that used such a schedule, please try to make
  it fully reproducible.

How should Adam’s hyperparameters be tuned?

[Click to expand]

As discussed above, making general statements about search spaces and how
many points one should sample from the search space is very difficult. Note
that not all the hyperparameters in Adam are equally important. The
following rules of thumb correspond to different "budgets" for the number of
trials in a study.
- If < 10 trials in a study, only tune the (base) learning rate.
- If 10-25 trials, tune learning rate and $\beta_1$.
- If 25+ trials, tune the learning rate, $\beta_1$ and $\epsilon$.
- If one can run substantially more than 25 trials, additionally tune
  $\beta_2$.

Why use quasi-random search instead of more sophisticated black box optimization algorithms during the exploration phase of tuning?

[Click to expand]

Quasi-random search (based on
low-discrepancy sequences)
is our preference over fancier black box optimization tools when used as
part of an iterative tuning process intended to maximize insight into the
tuning problem (what we refer to as the "exploration phase"). Bayesian
optimization and similar tools are more appropriate for the exploitation
phase.
Quasi-random search based on randomly shifted low-discrepancy sequences can
be thought of as "jittered, shuffled grid search", since it uniformly, but
randomly, explores a given search space and spreads out the search points
more than random search.
The advantages of quasi-random search over more sophisticated black box
optimization tools (e.g. Bayesian optimization, evolutionary algorithms)
include:
1. Sampling the search space non-adaptively makes it possible to change the
  tuning objective in post hoc analysis without rerunning experiments.
  - For example, we usually want to find the best trial in terms of
    validation error achieved at any point in training. But the
    non-adaptive nature of quasi-random search makes it possible to find
    the best trial based on final validation error, training error, or
    some alternative evaluation metric without rerunning any
    experiments.
2. Quasi-random search behaves in a consistent and statistically
  reproducible way.
  - It should be possible to reproduce a study from six months ago even
    if the implementation of the search algorithm changes, as long as it
    maintains the same uniformity properties. If using sophisticated
    Bayesian optimization software, the implementation might change in
    an important way between versions, making it much harder to
    reproduce an old search. It isn’t always possible to roll back to an
    old implementation (e.g. if the optimization tool is run as a
    service).
3. Its uniform exploration of the search space makes it easier to reason
  about the results and what they might suggest about the search space.
  - For example, if the best point in the traversal of quasi-random
    search is at the boundary of the search space, this is a good (but
    not foolproof) signal that the search space bounds should be
    changed. This section
    goes into more depth. However, an adaptive black box optimization
    algorithm might have neglected the middle of the search space
    because of some unlucky early trials even if it happens to contain
    equally good points, since it is this exact sort of non-uniformity
    that a good optimization algorithm needs to employ to speed up the
    search.
4. Running different numbers of trials in parallel versus sequentially will
  not produce statistically different results when using quasi-random
  search (or other non-adaptive search algorithms), unlike with adaptive
  algorithms.
5. More sophisticated search algorithms may not always handle infeasible
  points correctly, especially if they aren't designed with neural network
  hyperparameter tuning in mind.
6. Quasi-random search is simple and works especially well when many tuning
  trials will be running in parallel.
  - Anecdotally¹, it is very hard for an adaptive algorithm to beat a
    quasi-random search that has 2X its budget, especially when many
    trials need to be run in parallel (and thus there are very few
    chances to make use of previous trial results when launching new
    trials).
  - Without expertise in Bayesian optimization and other advanced black
    box optimization methods, we might not achieve the benefits they
    are, in principle, capable of providing. It is hard to benchmark
    advanced black box optimization algorithms in realistic deep
    learning tuning conditions. They are a very active area of current
    research, and the more sophisticated algorithms come with their own
    pitfalls for inexperienced users. Experts in these methods are able
    to get good results, but in high-parallelism conditions the search
    space and budget tend to matter a lot more.
That said, if our computational resources only allow a small number of
trials to run in parallel and we can afford to run many trials in sequence,
Bayesian optimization becomes much more attractive despite making our tuning
results harder to interpret.

Where can I find an implementation of quasi-random search?

[Click to expand]

Open-Source Vizier has an implementation
of quasi-random search. Set algorithm="QUASI_RANDOM_SEARCH" in this usage example.
An alternative implementation exists
here.
Both implementations above generate a Halton sequence for a given search space (intended to
implement a shifted, scrambled Halton sequence as recommended in
https://arxiv.org/abs/1706.03200).
If a quasi-random search algorithm based on a low-discrepancy sequence is
not available, it is possible to substitute pseudo random uniform search
instead, although this is likely to be slightly less efficient.
- In 1-2 dimensions, grid search is also acceptable, although not in
  higher dimensions (see
  Bergstra & Bengio, 2012).

How many trials are needed to get good results with quasi-random search?

[Click to expand]

A box plot showing the importance of sampling enough

Figure 3: A ResNet-50 was tuned on ImageNet with 100 trials. Via bootstrapping, different amounts of tuning budget were simulated. Box plots of the best performances for each trial budget are plotted above.

There is no way to answer this question in general, but we can look at
specific examples.
As the Figure 3 shows, the number of trials in a study can have a
substantial impact on the results.
- Notice how large the interquartile ranges are when 6 trials were
  sampled, versus when 20 trials were sampled.
- Even with 20 trials, it is likely that the difference between especially
  lucky and unlucky studies will be larger than the typical variation
  between re-trains of this model on different random seeds, with fixed
  hyperparameters, which for this workload might be around +/- 0.1% on a
  validation error rate of ~23%.

How can optimization failures be debugged and mitigated?

[Click to expand]

Summary: If the model is experiencing optimization difficulties, it’s
important to fix them before trying other things. Diagnosing and correcting
training failures is an active area of research.

Changing the strides in a single residual block in a WideResnet results in training instability.

Figure 4: Changing the strides in a single residual block (2x2 -> 1x1) in a WideResnet results in training instability. This does not degrade performance at low learning rates, but high learning rates no longer train well due to the instability. Applying 1000 steps of learning rate warmup resolves this particular instance of instability, allowing stable training at max learning rate of .1.

Identifying unstable workloads

Any workload will become unstable if the learning rate is too large.
Instability is only an issue when it forces us to use a learning rate that’s
too small.
There are at least two types of training instability worth distinguishing:
1. Instability at initialization/early in training.
2. Sudden instability in the middle of training.
We can take a systematic approach to identifying stability issues in our
workload.
1. Do a learning rate sweep and find the best learning rate lr*.
2. Plot training loss curves for learning rates just above lr*.
3. If the learning rates > lr* show loss instability (loss goes up not down
  during periods of training), then it is likely that fixing the
  instability will result in better training.
Log the L2 norm of the full loss gradient during training, outlier values
can result in spurious instability in the middle of training. This can
inform how to pick gradient/update clipping.

NOTE: Some models show very early instability followed by a recovery that
results in slow but stable training. Common evaluation schedules can miss
these issues by not evaluating frequently enough!

To check for this, we can train for an abbreviated run of just ~500 steps using
lr = 2 * current best, but evaluate every step.

Illustration of the value of more frequent evaluations at the start of
training.

Figure 5: Illustration of the value of more frequent evaluations at the start of training. Useful if there’s a suspicion that the model suffers from early training instability.

Potential fixes for common instability patterns

Apply learning rate warmup
- Best for early training instability.
Apply gradient clipping
- Good for both early and mid training instability, may fix some bad inits
  that warmup cannot.
Try a new optimizer
- Sometimes Adam can handle instabilities that Momentum can’t. This is an
  active area of research.
We can ensure that we’re using best practices/initializations for our model
architecture (examples below).
- Add residual connections and normalization if the model doesn't contain
  it already.
Normalization should be the last operation before the residual. E.g. x +
Norm(f(x)).
Norm(x + f(x)) known to cause issues.
Try initializing residual branches to 0 (e.g.
ReZero init).
Lower the learning rate
- This is a last resort.

Learning rate warmup

An example of instability during a warmup period (note the horizontal axis log
scale).

Figure 6: An example of instability during a warmup period (note the horizontal axis log scale). 40k steps of warmup was needed for successful training in this case.

When to apply learning rate warmup

Axis plot for model with instability

Figure 7a: An example of a hyperparameter axis plot for a model exhibiting training instability. The best learning rate is at the edge of what is feasible. An "infeasible" trial is defined as one that either produces NaNs or uncharacteristically high values of the loss.

Loss curve for model with instability

Figure 7b: The training loss of a model trained with a learning rate where we see instability.

Figure 7a shows a hyperparameter axis plot that indicates a model
experiencing optimization instabilities, because the best learning rate is
right at the edge of instability.
Figure 7b shows how this can be double-checked by examining the training
loss of a model trained with a learning rate either 5x or 10x larger than
this peak. If that plot shows a sudden rise in the loss after a steady
decline (e.g. at step ~10k in the figure above), then the model likely
suffers from optimization instability.

How to apply learning rate warmup

Beneficial effect of warmup on training instabilities

Figure 8: Beneficial effect of learning rate warmup on addressing training instabilities.

Using the section immediately above, we assume that the practitioner has
already identified the learning rate at which the model becomes unstable.
This is the unstable_base_learning_rate.
Warmup involves prepending a learning rate schedule that ramps up the
learning rate from 0 to some stable base_learning_rate, that is at least
one order of magnitude larger than unstable_base_learning_rate. The
default would be to try a base_learning_rate that’s 10x
unstable_base_learning_rate. Although note that it’d be possible to run
this entire procedure again for something like 100x
unstable_base_learning_rate. The specific schedule is:
- Ramp up from 0 to base_learning_rate over warmup_steps.
- Train at a constant rate for post_warmup_steps.
Our goal is to find the shortest number of warmup_steps that allows us to
access peak learning rates that are much higher than
unstable_base_learning_rate.
So for each base_learning_rate, we need to tune warmup_steps and
post_warmup_steps. It’s usually fine to set post_warmup_steps to be
2*warmup_steps.
Warmup can be tuned independently of an existing decay schedule.
warmup_steps should be swept at a few different orders of magnitude. For
example, an example study could try [10, 10³, 10⁴,
10⁵]. The largest feasible point shouldn't be more than 10% of
max_train_steps.
Once a warmup_steps that doesn't blow up training at base_learning_rate
has been established, it should be applied to the baseline model.
Essentially, we prepend this schedule onto the existing schedule, and use
the optimal checkpoint selection discussed above to compare this experiment
to the baseline. For example, if we originally had 10,000 max_train_steps
and did warmup_steps for 1000 steps, the new training procedure should run
for 11,000 steps total.
If long warmup_steps are required for stable training (>5% of
max_train_steps), max_train_steps may need to be increased to account
for this.
There isn't really a "typical" value across the full range of workloads.
Some models only need 100 steps, while others (particularly transformers)
may need 40k+.

Gradient clipping

Gradient clipping on early training instabilities

Figure 9: Illustration of gradient clipping correcting early training instability.

Gradient clipping is most useful when large or outlier gradient issues
occur.
Clipping can fix either early training instability (large gradient norm
early), or mid training instabilities (sudden gradient spikes mid training).
Sometimes longer warmup periods can correct instabilities that clipping does
not: see this section above.
- 🤖 What about clipping during warmup?
The ideal clip thresholds are just above the "typical" gradient norm.
Here’s an example of how gradient clipping could be done:
- If the norm of the gradient $\left | g \right |$ is greater than the
  gradient clipping threshold $\lambda$, then do ${g}'= \lambda \times \frac{g}{\left | g \right |}$ where ${g}'$ is the new gradient.
Log the unclipped gradient norm during training. By default, generate:
- A plot of gradient norm vs step
- A histogram of gradient norms aggregated over all steps
Choose a gradient clipping threshold based on the 90th percentile of
gradient norms.
- The threshold will be workload dependent, but 90% is a good starting
  point. If it doesn't work, this threshold can be tuned.
- 🤖 What about some sort of adaptive strategy?
If we try gradient clipping and the instability issues remain, we can try it
harder (i.e. make the threshold smaller).
Extremely aggressive gradient clipping is in essence a strange way of
reducing the learning rate. If we find ourselves using extremely aggressive
clipping, we probably should just cut the learning rate instead.
We would usually consider having >50% of the updates getting clipped somehow
as "extremely aggressive".
If we need to do extremely aggressive gradient clipping to deal with our
instability issues, then we might as well reduce the learning rate.

Why do you call the learning rate and other optimization parameters hyperparameters? They are not parameters of any prior distribution.

[Click to expand]

It is true that the term "hyperparameter" has a precise
meaning in Bayesian machine
learning and referring to the learning rate and most of the other parameters
we tune in deep learning as "hyperparameters" is an abuse of terminology.
We would prefer to use the term "metaparameter" for learning rates,
architectural parameters, and all the other things we tune in deep learning,
since it avoids the potential for confusion that comes from misusing the
word "hyperparameter" (confusion that is especially likely when discussing
Bayesian optimization where the probabilistic response surface models have
their own true hyperparameters).
Unfortunately, although potentially confusing, the term hyperparameter has become
extremely common in the deep learning community.
Therefore, for a document, such as this one, intended for a wide audience
that includes many people who are unlikely to be aware of this technicality,
we made the choice to contribute to one source of confusion in the
field in hopes of avoiding another.
That said, we might make a different choice when publishing a research
paper, and we would encourage others to use "metaparameter" instead in most
contexts.

Why shouldn't the batch size be tuned to directly improve validation set performance?

[Click to expand]

Changing the batch size without changing any other details of the training pipeline will often affect the validation set performance.
However, the difference in validation set performance between two batch sizes typically goes away if the training pipeline is optimized independently for each batch size.
The hyperparameters that interact most strongly with the batch size, and therefore are most important to tune separately for each batch size, are the optimizer hyperparameters (e.g. learning rate, momentum) and the regularization hyperparameters.
- Smaller batch sizes introduce more noise into the training algorithm due to sample variance, and this noise can have a regularizing effect. Thus, larger batch sizes can be more prone to overfitting and may require stronger regularization and/or additional regularization techniques.
In addition, the number of training steps may need to be adjusted when changing the batch size.
Once all these effects are taken into account, there is currently no convincing evidence that the batch size affects the maximum achievable validation performance (see Shallue et al. 2018).

What are the update rules for all the popular optimization algorithms?

[Click to expand]

Stochastic gradient descent (SGD)

$$\theta_{t+1} = \theta_{t} - \eta_t \nabla \mathcal{l}(\theta_t)$$

Momentum

$$v_0 = 0$$

$$v_{t+1} = \gamma v_{t} + \nabla \mathcal{l}(\theta_t)$$

$$\theta_{t+1} = \theta_{t} - \eta_t v_{t+1}$$

Nesterov

$$v_0 = 0$$

$$v_{t+1} = \gamma v_{t} + \nabla \mathcal{l}(\theta_t)$$

$$\theta_{t+1} = \theta_{t} - \eta_t( \gamma v_{t+1} + \nabla \mathcal{l}(\theta_{t})$$

RMSProp

$$v_0 = 1 \text{,} m_0 = 0$$

$$v_{t+1} = \rho v_{t} + (1 - \rho) \nabla \mathcal{l}(\theta_t)^2$$

$$m_{t+1} = \gamma m_{t} + \frac{\eta_t}{\sqrt{v_{t+1} + \epsilon}}\nabla \mathcal{l}(\theta_t)$$

$$\theta_{t+1} = \theta_{t} - m_{t+1}$$

ADAM

$$m_0 = 0 \text{,} v_0 = 0$$

$$m_{t+1} = \beta_1 m_{t} + (1 - \beta_1) \nabla \mathcal{l} (\theta_t)$$

$$v_{t+1} = \beta_2 v_{t} + (1 - \beta_2) \nabla \mathcal{l}(\theta_t)^2$$

$$b_{t+1} = \frac{\sqrt{1 - \beta_2^{t+1}}}{1 - \beta_1^{t+1}}$$

$$\theta_{t+1} = \theta_{t} - \alpha_t \frac{m_{t+1}}{\sqrt{v_{t+1}} + \epsilon} b_{t+1}$$

NADAM

$$m_0 = 0 \text{,} v_0 = 0$$

$$m_{t+1} = \beta_1 m_{t} + (1 - \beta_1) \nabla \mathcal{l} (\theta_t)$$

$$v_{t+1} = \beta_2 v_{t} + (1 - \beta_2) \nabla \mathcal{l} (\theta_t)^2$$

$$b_{t+1} = \frac{\sqrt{1 - \beta_2^{t+1}}}{1 - \beta_1^{t+1}}$$

$$\theta_{t+1} = \theta_{t} - \alpha_t \frac{\beta_1 m_{t+1} + (1 - \beta_1) \nabla \mathcal{l} (\theta_t)}{\sqrt{v_{t+1}} + \epsilon} b_{t+1}$$

Acknowledgments

We owe a debt of gratitude to Max Bileschi, Roy Frostig, Zelda Mariet, Stan
Bileschi, Mohammad Norouzi, Chris DuBois and Charles Sutton for reading the
manuscript and providing valuable feedback.
We reused some experimental data for several plots that were originally
produced by Naman Agarwal for other joint research.
We would like to thank Will Chen for invaluable advice on the presentation of the document.
We would also like to thank Rohan Anil for useful discussions.

Citing

@misc{tuningplaybookgithub,
  author = {Varun Godbole and George E. Dahl and Justin Gilmer and Christopher J. Shallue and Zachary Nado},
  title = {Deep Learning Tuning Playbook},
  url = {http://github.com/google-research/tuning_playbook},
  year = {2023},
  note = {Version 1.0}
}

Contributing

This is not an officially supported Google product.
We'd love to hear your feedback!
- If you like the playbook, please leave a star! Or email
  deep-learning-tuning-playbook [at] googlegroups.com. Testimonials help
  us justify creating more resources like this.
- If anything seems incorrect, please file an issue to start a discussion.
  For questions or other messages where an issue isn't appropriate, please
  open a new discussion topic on GitHub.
As discussed in the preamble, this is a living document. We anticipate
making periodic improvements, both small and large. If you’d like to be
notified, please watch our repository (see instructions).
Please don't file a pull request without first coordinating with the authors
via the issue tracking system.

Contributor License Agreement

Contributions to this project must be accompanied by a Contributor License
Agreement (CLA). You (or your employer) retain the copyright to your
contribution; this simply gives us permission to use and redistribute your
contributions as part of the project. Head over to
https://cla.developers.google.com/ to see your current agreements on file or
to sign a new one.

You generally only need to submit a CLA once, so if you've already submitted one
(even if it was for a different project), you probably don't need to do it
again.

Code Reviews

All submissions, including submissions by project members, require review. We
use GitHub pull requests for this purpose. Consult
GitHub Help for more
information on using pull requests.

Community Guidelines

This project follows
Google's Open Source Community Guidelines.

Ben Recht and Kevin Jamieson
pointed out how strong
2X-budget random search is as a baseline (the
Hyperband paper
makes similar arguments), but it is certainly possible to find search
spaces and problems where state-of-the-art Bayesian optimization
techniques crush random search that has 2X the budget. However, in our
experience beating 2X-budget random search gets much harder in the
high-parallelism regime since Bayesian optimization has no opportunity to
observe the results of previous trials. ↩︎

No Description

BibTeX

ahmed.m.omran@gmail.com 1061099+varungodbole@users.noreply.github.com georgedahl@users.noreply.github.com you@example.com 124639423+AminMohamed-3@users.noreply.github.com cshallue@users.noreply.github.com mikegtrm@gmail.com 11041768+oscmansan@users.noreply.github.com mail@sebastianraschka.com znado@users.noreply.github.com

How to access data resources in code

README.md

Deep Learning Tuning Playbook

Table of Contents

Who is this document for?

Why a tuning playbook?

Guide for starting a new project

Choosing the model architecture

Choosing the optimizer

Choosing the batch size

Determining the feasible batch sizes and estimating training throughput

Choosing the batch size to minimize training time

Choosing the batch size to minimize resource consumption

Changing the batch size requires re-tuning most hyperparameters

How batch norm interacts with the batch size

Choosing the initial configuration

A scientific approach to improving model performance

The incremental tuning strategy

Exploration vs exploitation

Choosing the goal for the next round of experiments

Designing the next round of experiments

Identifying scientific, nuisance, and fixed hyperparameters

Creating a set of studies

Striking a balance between informative and affordable experiments

Extracting insight from experimental results

Identifying bad search space boundaries

Not sampling enough points in the search space

Examining the training curves

Detecting whether a change is useful with isolation plots

Automate generically useful plots

Determining whether to adopt a training pipeline change or hyperparameter configuration

After exploration concludes

Determining the number of steps for each training run

Deciding how long to train when training is not compute-bound

Algorithm for picking an initial candidate for max_train_steps using a learning rate sweep

Deciding how long to train when training is compute-bound

Round 1

Round 2

Additional guidance for the training pipeline

Optimizing the input pipeline

Evaluating model performance

Evaluation settings

Setting up periodic evaluations

Choosing a sample for periodic evaluation

Saving checkpoints and retrospectively selecting the best checkpoint

Setting up experiment tracking

Batch normalization implementation details

Considerations for multi-host pipelines

FAQs

What is the best learning rate decay schedule family?

Which learning rate decay should I use as a default?

Why do some papers have complicated learning rate schedules?

How should Adam’s hyperparameters be tuned?

Why use quasi-random search instead of more sophisticated black box optimization algorithms during the exploration phase of tuning?

Where can I find an implementation of quasi-random search?

How many trials are needed to get good results with quasi-random search?

How can optimization failures be debugged and mitigated?

Identifying unstable workloads

Potential fixes for common instability patterns

Learning rate warmup

When to apply learning rate warmup

How to apply learning rate warmup

Gradient clipping

Why do you call the learning rate and other optimization parameters hyperparameters? They are not parameters of any prior distribution.

Why shouldn't the batch size be tuned to directly improve validation set performance?

What are the update rules for all the popular optimization algorithms?

Stochastic gradient descent (SGD)

Momentum

Nesterov

RMSProp

ADAM

NADAM

Acknowledgments

Citing

Contributing

Contributor License Agreement

Code Reviews

Community Guidelines

Contributors (10) All

Contributors (10)
All