Tune a CNN on MNIST
This tutorial walks through using Ax to tune two hyperparameters (learning rate and momentum) for a PyTorch CNN on the MNIST dataset trained using SGD with momentum.
import sys
in_colab = 'google.colab' in sys.modules
if in_colab:
%pip install ax-platform
import torch
import torch.nn as nn
import torch.nn.functional as F
from ax.service.ax_client import AxClient, ObjectiveProperties
from ax.service.utils.report_utils import exp_to_df
from ax.utils.notebook.plotting import init_notebook_plotting, render
from ax.utils.tutorials.cnn_utils import evaluate, load_mnist, train
from torch._tensor import Tensor
from torch.utils.data import DataLoader
import plotly.io as pio
init_notebook_plotting()
if in_colab:
pio.renderers.default = "colab"
torch.manual_seed(42)
dtype = torch.float
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
1. Load MNIST data
First, we need to load the MNIST data and partition it into training, validation, and test sets.
Note: this will download the dataset if necessary.
BATCH_SIZE = 512
train_loader, valid_loader, test_loader = load_mnist(batch_size=BATCH_SIZE)
2. Initialize Client
Create a client object to interface with Ax APIs. By default this runs locally without storage.
ax_client = AxClient()
3. Set up experiment
An experiment consists of a search space (parameters and parameter constraints) and optimization configuration (objective name, minimization setting, and outcome constraints).
# Create an experiment with required arguments: name, parameters, and objective_name.
ax_client.create_experiment(
name="tune_cnn_on_mnist", # The name of the experiment.
parameters=[
{
"name": "lr", # The name of the parameter.
"type": "range", # The type of the parameter ("range", "choice" or "fixed").
"bounds": [1e-6, 0.4], # The bounds for range parameters.
# "values" The possible values for choice parameters .
# "value" The fixed value for fixed parameters.
"value_type": "float", # Optional, the value type ("int", "float", "bool" or "str"). Defaults to inference from type of "bounds".
"log_scale": True, # Optional, whether to use a log scale for range parameters. Defaults to False.
# "is_ordered" Optional, a flag for choice parameters.
},
{
"name": "momentum",
"type": "range",
"bounds": [0.0, 1.0],
},
],
objectives={"accuracy": ObjectiveProperties(minimize=False)}, # The objective name and minimization setting.
# parameter_constraints: Optional, a list of strings of form "p1 >= p2" or "p1 + p2 <= some_bound".
# outcome_constraints: Optional, a list of strings of form "constrained_metric <= some_bound".
)
4. Define how to evaluate trials
First we define a simple CNN class to classify the MNIST images
class CNN(nn.Module):
def __init__(self) -> None:
super().__init__()
self.conv1 = nn.Conv2d(1, 20, kernel_size=5, stride=1)
self.fc1 = nn.Linear(8 * 8 * 20, 64)
self.fc2 = nn.Linear(64, 10)
def forward(self, x: Tensor) -> Tensor:
x = F.relu(self.conv1(x))
x = F.max_pool2d(x, 3, 3)
x = x.view(-1, 8 * 8 * 20)
x = F.relu(self.fc1(x))
x = self.fc2(x)
return F.log_softmax(x, dim=-1)
In this tutorial, we want to optimize classification accuracy on the validation set as a
function of the learning rate and momentum. The train_evaluate
function takes in a
parameterization (set of parameter values), computes the classification accuracy, and
returns that metric.
def train_evaluate(parameterization):
"""
Train the model and then compute an evaluation metric.
In this tutorial, the CNN utils package is doing a lot of work
under the hood:
- `train` initializes the network, defines the loss function
and optimizer, performs the training loop, and returns the
trained model.
- `evaluate` computes the accuracy of the model on the
evaluation dataset and returns the metric.
For your use case, you can define training and evaluation functions
of your choosing.
"""
net = CNN()
net = train(
net=net,
train_loader=train_loader,
parameters=parameterization,
dtype=dtype,
device=device,
)
return evaluate(
net=net,
data_loader=valid_loader,
dtype=dtype,
device=device,
)
5. Run optimization loop
First we use attach_trial
to attach a custom trial with manually-chosen parameters.
This step is optional, but we include it here to demonstrate adding manual trials and to
serve as a baseline model with decent performance.
# Attach the trial
ax_client.attach_trial(
parameters={"lr": 0.000026, "momentum": 0.58}
)
# Get the parameters and run the trial
baseline_parameters = ax_client.get_trial_parameters(trial_index=0)
ax_client.complete_trial(trial_index=0, raw_data=train_evaluate(baseline_parameters))
Now we start the optimization loop.
At each step, the user queries the client for a new trial then submits the evaluation of that trial back to the client.
Note that Ax auto-selects an appropriate optimization algorithm based on the search
space. For more advanced use cases that require a specific optimization algorithm, pass
a generation_strategy
argument into the AxClient
constructor. Note that when
Bayesian Optimization is used, generating new trials may take a few minutes.
for i in range(25):
parameters, trial_index = ax_client.get_next_trial()
# Local evaluation here can be replaced with deployment to external system.
ax_client.complete_trial(trial_index=trial_index, raw_data=train_evaluate(parameters))
How many trials can run in parallel?
By default, Ax restricts number of trials that can run in parallel for some optimization stages, in order to improve the optimization performance and reduce the number of trials that the optimization will require. To check the maximum parallelism for each optimization stage:
ax_client.get_max_parallelism()
The output of this function is a list of tuples of form (number of trials, max parallelism), so the example above means "the max parallelism is 5 for the first 5 trials and 3 for all subsequent trials." This is because the first 5 trials are produced quasi-randomly and can all be evaluated at once, and subsequent trials are produced via Bayesian optimization, which converges on optimal point in fewer trials when parallelism is limited. MaxParallelismReachedException indicates that the parallelism limit has been reached –– refer to the 'Service API Exceptions Meaning and Handling' section at the end of the tutorial for handling.
How to view all existing trials during optimization?
ax_client.get_trials_data_frame()
trial_index | arm_name | trial_status | generation_method | generation_node | accuracy | lr | momentum | |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0_0 | COMPLETED | nan | nan | 0.841833 | 2.6e-05 | 0.58 |
1 | 1 | 1_0 | COMPLETED | Sobol | GenerationStep_0 | 0.100333 | 0.009955 | 0.633423 |
2 | 2 | 2_0 | COMPLETED | Sobol | GenerationStep_0 | 0.884333 | 9e-05 | 0.335441 |
3 | 3 | 3_0 | COMPLETED | Sobol | GenerationStep_0 | 0.678667 | 2e-06 | 0.902833 |
4 | 4 | 4_0 | COMPLETED | Sobol | GenerationStep_0 | 0.100333 | 0.10174 | 0.065787 |
5 | 5 | 5_0 | COMPLETED | Sobol | GenerationStep_0 | 0.088167 | 0.017004 | 0.802601 |
6 | 6 | 6_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.774 | 3.5e-05 | 0 |
7 | 7 | 7_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.9055 | 8.3e-05 | 1 |
8 | 8 | 8_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.8565 | 4.8e-05 | 1 |
9 | 9 | 9_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.486167 | 0.00015 | 1 |
10 | 10 | 10_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.8575 | 1.3e-05 | 1 |
11 | 11 | 11_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.622667 | 1.1e-05 | 0 |
12 | 12 | 12_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.887167 | 7e-05 | 0.253302 |
13 | 13 | 13_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.133333 | 1e-06 | 0 |
14 | 14 | 14_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.849833 | 0.000139 | 0 |
15 | 15 | 15_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.828167 | 5e-06 | 1 |
16 | 16 | 16_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.827 | 1.9e-05 | 1 |
17 | 17 | 17_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.874 | 3.9e-05 | 0.566309 |
18 | 18 | 18_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.810667 | 7.5e-05 | 0 |
19 | 19 | 19_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.883667 | 2.4e-05 | 0.763182 |
20 | 20 | 20_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.8355 | 0.000286 | 0 |
21 | 21 | 21_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.881 | 5.7e-05 | 0.448405 |
22 | 22 | 22_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.888167 | 2.8e-05 | 0.805158 |
23 | 23 | 23_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.405333 | 0.000838 | 0 |
24 | 24 | 24_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.873667 | 5.1e-05 | 0.337101 |
25 | 25 | 25_0 | COMPLETED | BoTorch | GenerationStep_1 | 0.897833 | 6.8e-05 | 0.740126 |
6. Retrieve best parameters
Once it's complete, we can access the best parameters found, as well as the corresponding metric values. Note that these parameters may not necessarily be the set that yielded the highest observed accuracy because Ax uses the highest model predicted accuracy to choose the best parameters (see here for more details). Due to randomness in the data or the algorithm itself, using observed accuracy may result in choosing an outlier for the best set of parameters. Using the model predicted best will use the model to regularize the observations and reduce the likelihood of picking some outlier in the data.
best_parameters, values = ax_client.get_best_parameters()
best_parameters
mean, covariance = values
mean
7. Plot the response surface and optimization trace
Contour plot showing classification accuracy as a function of the two hyperparameters.
The black squares show points that we have actually run; notice how they are clustered in the optimal region.
render(ax_client.get_contour_plot(param_x="lr", param_y="momentum", metric_name="accuracy"))
Here we plot the optimization trace, showing the progression of finding the point with the optimal objective:
render(
ax_client.get_optimization_trace()
)
8. Train CNN with best hyperparameters and evaluate on test set
Note that the resulting accuracy on the test set generally won't be the same as the maximum accuracy achieved on the evaluation set throughout optimization.
df = ax_client.get_trials_data_frame()
best_arm_idx = df.trial_index[df["accuracy"] == df["accuracy"].max()].values[0]
best_arm = ax_client.get_trial_parameters(best_arm_idx)
best_arm
combined_train_valid_set = torch.utils.data.ConcatDataset(
[
train_loader.dataset.dataset,
valid_loader.dataset.dataset,
]
)
combined_train_valid_loader = torch.utils.data.DataLoader(
combined_train_valid_set,
batch_size=BATCH_SIZE,
shuffle=True,
)
net = train(
net=CNN(),
train_loader=combined_train_valid_loader,
parameters=best_arm,
dtype=dtype,
device=device,
)
test_accuracy = evaluate(
net=net,
data_loader=test_loader,
dtype=dtype,
device=device,
)
print(f"Classification Accuracy (test set): {round(test_accuracy*100, 2)}%")
9. Save / reload optimization to JSON / SQL
We can serialize the state of optimization to JSON and save it to a .json
file or save
it to the SQL backend. For the former:
ax_client.save_to_json_file() # For custom filepath, pass `filepath` argument.
restored_ax_client = (
AxClient.load_from_json_file()
) # For custom filepath, pass `filepath` argument.
To store state of optimization to an SQL backend, first follow setup instructions on Ax website.
Having set up the SQL backend, pass DBSettings
to AxClient
on instantiation (note
that SQLAlchemy
dependency will have to be installed – for installation, refer to
optional dependencies on
Ax website):
from ax.storage.sqa_store.structs import DBSettings
# URL is of the form "dialect+driver://username:password@host:port/database".
db_settings = DBSettings(url="sqlite:///foo.db")
# Instead of URL, can provide a `creator function`; can specify custom encoders/decoders if necessary.
new_ax = AxClient(db_settings=db_settings)
When valid DBSettings
are passed into AxClient
, a unique experiment name is a
required argument (name
) to ax_client.create_experiment
. The state of the
optimization is auto-saved any time it changes (i.e. a new trial is added or
completed, etc).
To reload an optimization state later, instantiate AxClient
with the same DBSettings
and use ax_client.load_experiment_from_database(experiment_name="my_experiment")
.
Special Cases
Evaluation failure: should any optimization iterations fail during evaluation,
log_trial_failure
will ensure that the same trial is not proposed again.
_, trial_index = ax_client.get_next_trial()
ax_client.log_trial_failure(trial_index=trial_index)
Need to run many trials in parallel: for optimal results and optimization
efficiency, we strongly recommend sequential optimization (generating a few trials, then
waiting for them to be completed with evaluation data). However, if your use case needs
to dispatch many trials in parallel before they are updated with data and you are
running into the "All trials for current model have been generated, but not enough data
has been observed to fit next model" error, instantiate AxClient
as
AxClient(enforce_sequential_optimization=False)
.
Service API Exceptions Meaning and Handling
DataRequiredError
:
Ax generation strategy needs to be updated with more data to proceed to the next
optimization model. When the optimization moves from initialization stage to the
Bayesian optimization stage, the underlying BayesOpt model needs sufficient data to
train. For optimal results and optimization efficiency (finding the optimal point in the
least number of trials), we recommend sequential optimization (generating a few trials,
then waiting for them to be completed with evaluation data). Therefore, the correct way
to handle this exception is to wait until more trial evaluations complete and log their
data via ax_client.complete_trial(...)
.
However, if there is strong need to generate more trials before more data is available,
instantiate AxClient
as AxClient(enforce_sequential_optimization=False)
. With this
setting, as many trials will be generated from the initialization stage as requested,
and the optimization will move to the BayesOpt stage whenever enough trials are
completed.
MaxParallelismReachedException
:
generation strategy restricts the number of trials that can be run simultaneously (to
encourage sequential optimization), and the parallelism limit has been reached. The
correct way to handle this exception is the same as DataRequiredError
– to wait until
more trial evluations complete and log their data via ax_client.complete_trial(...)
.
In some cases higher parallelism is important, so
enforce_sequential_optimization=False
kwarg to AxClient allows the user to suppress
limiting of parallelism. It's also possible to override the default parallelism setting
for all stages of the optimization by passing choose_generation_strategy_kwargs
to
ax_client.create_experiment
:
ax_client = AxClient()
ax_client.create_experiment(
parameters=[
{"name": "x", "type": "range", "bounds": [-5.0, 10.0]},
{"name": "y", "type": "range", "bounds": [0.0, 15.0]},
],
# Sets max parallelism to 10 for all steps of the generation strategy.
choose_generation_strategy_kwargs={"max_parallelism_override": 10},
)
ax_client.get_max_parallelism() # Max parallelism is now 10 for all stages of the optimization.