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Hyperparameter Optimization

This document provides a walkthrough of the hyperparameter optimization example. To run the application, first install this dependency.

Then from the directory ray/examples/hyperopt/ run the following.

source ../../setup-env.sh
python driver.py

Machine learning algorithms often have a number of hyperparameters whose values must be chosen by the practitioner. For example, an optimization algorithm may have a step size, a decay rate, and a regularization coefficient. In a deep network, the network parameterization itself (e.g., the number of layers and the number of units per layer) can be considered a hyperparameter.

Choosing these parameters can be challenging, and so a common practice is to search over the space of hyperparameters. One approach that works surprisingly well is to randomly sample different options.

The serial version

Suppose that we want to train a convolutional network, but we aren't sure how to choose the following hyperparameters:

  • the learning rate
  • the batch size
  • the dropout probability
  • the standard deviation of the distribution from which to initialize the network weights

Suppose that we've defined a Python function train_cnn_and_compute_accuracy, which takes values for these hyperparameters as its input (along with the dataset), trains a convolutional network using those hyperparameters, and returns the accuracy of the trained model on a validation set.

def train_cnn_and_compute_accuracy(hyperparameters, train_images, train_labels, validation_images, validation_labels):
  # Construct a deep network, train it, and return the validation accuracy.
  # The argument hyperparameters is a dictionary with keys:
  #   - "learning_rate"
  #   - "batch_size"
  #   - "dropout"
  #   - "stddev"
  return validation_accuracy

Something that works surprisingly well is to try random values for the hyperparameters. For example, we can write the following.

def generate_random_params():
  # Randomly choose values for the hyperparameters
  learning_rate = 10 ** np.random.uniform(-5, 5)
  batch_size = np.random.randint(1, 100)
  dropout = np.random.uniform(0, 1)
  stddev = 10 ** np.random.uniform(-5, 5)
  return {"learning_rate": learning_rate, "batch_size": batch_size, "dropout": dropout, "stddev": stddev}

results = []
for _ in range(100):
  params = generate_random_params()
  accuracy = train_cnn_and_compute_accuracy(randparams, train_images, train_labels, validation_images, validation_labels)
  results.append(accuracy)

Then we can inspect the contents of results and see which set of hyperparameters worked the best.

Of course, as there are no dependencies between the different invocations of train_cnn_and_compute_accuracy, this computation could easily be parallelized over multiple cores or multiple machines. Let's do that now.

The distributed version

First, let's turn train_cnn_and_compute_accuracy into a remote function in Ray by writing it as follows. In this example application, a slightly more complicated version of this remote function is defined in hyperopt.py.

@ray.remote
def train_cnn_and_compute_accuracy(hyperparameters, train_images, train_labels, validation_images, validation_labels):
  # Actual work omitted.
  return validation_accuracy

The only difference is that we added the @ray.remote decorator.

Now a call to train_cnn_and_compute_accuracy does not execute the function. It submits the task to the scheduler and returns an object ID for the output of the eventual computation. The scheduler, at its leisure, will schedule the task on a worker (which may live on the same machine or on a different machine in the cluster).

Now the for loop runs almost instantaneously because it does not do any actual computation. Instead, it simply submits a number of tasks to the scheduler.

result_ids = []
# Launch 100 tasks.
for _ in range(100):
  params = generate_random_params()
  accuracy_id = train_cnn_and_compute_accuracy.remote(randparams, train_images, train_labels, validation_images, validation_labels)
  result_ids.append(accuracy_id)

If we wish to wait until the results have all been retrieved, we can retrieve their values with ray.get.

results = ray.get(result_ids)

One drawback of the above approach is that nothing will be printed until all of the experiments have finished. What we'd really like is to start processing the results of certain experiments as soon as they finish (and possibly launch more experiments based on the outcomes of the first ones). To do this, we can use ray.wait, which takes a list of object IDs and returns two lists of object IDs.

ready_ids, remaining_ids = ray.wait(result_ids, num_returns=3, timeout=10)

In the above, result_ids is a list of object IDs. The command ray.wait will return as soon as either three of the object IDs in result_ids are ready (that is, the task that created the corresponding object finished executing and stored the object in the object store) or ten seconds pass, whichever comes first. To wait indefinitely, omit the timeout argument. Now, we can rewrite the script as follows.

remaining_ids = []
# Launch 100 tasks.
for _ in range(100):
  params = generate_random_params()
  accuracy_id = train_cnn_and_compute_accuracy.remote(randparams, train_images, train_labels, validation_images, validation_labels)
  remaining_ids.append(accuracy_id)

# Process the tasks one at a time.
while len(remaining_ids) > 0:
  # Process the next task that finishes.
  ready_ids, remaining_ids = ray.wait(remaining_ids, num_returns=1)
  # Get the accuracy corresponding to the ready object ID.
  accuracy = ray.get(ready_ids[0])
  print "Accuracy {}".format(accuracy)

Note that the above example does not associate the accuracy with the parameters that produced that accuracy, but this is done in the actual script.

Additional notes

Early Stopping: Sometimes when running an optimization, it is clear early on that the hyperparameters being used are bad (for example, the loss function may start diverging). In these situations, it makes sense to end that particular run early to save resources. This is implemented within the remote function train_cnn_and_compute_accuracy. If it detects that the optimization is going poorly, it returns early.