Learning Rate Scheduling

The learning rate is considered one of the most important hyperparameters for training deep neural networks, but choosing it can be quite hard. Rather than simply using a fixed learning rate, it is common to use a learning rate scheduler. In this example, we will use the cosine scheduler. Before the cosine scheduler comes into play, we start with a so-called warmup period in which the learning rate increases linearly for warmup_epochs epochs. For more information about the cosine scheduler, check out the paper “SGDR: Stochastic Gradient Descent with Warm Restarts”.

We will show you how to…

  • define a learning rate schedule

  • train a simple model using that schedule

def create_learning_rate_fn(config, base_learning_rate, steps_per_epoch):
  """Creates learning rate schedule."""
  warmup_fn = optax.linear_schedule(
      init_value=0., end_value=base_learning_rate,
      transition_steps=config.warmup_epochs * steps_per_epoch)
  cosine_epochs = max(config.num_epochs - config.warmup_epochs, 1)
  cosine_fn = optax.cosine_decay_schedule(
      init_value=base_learning_rate,
      decay_steps=cosine_epochs * steps_per_epoch)
  schedule_fn = optax.join_schedules(
      schedules=[warmup_fn, cosine_fn],
      boundaries=[config.warmup_epochs * steps_per_epoch])
  return schedule_fn

To use the schedule, we must create a learning rate function by passing the hyperparameters to the create_learning_rate_fn function and then pass the function to your Optax optimizer. For example using this schedule on MNIST would require changing the train_step function:

Default learning rate

Learning rate schedule

@jax.jit
def train_step(state, batch):
  def loss_fn(params):
    logits = CNN().apply({'params': params}, batch['image'])
    one_hot = jax.nn.one_hot(batch['label'], 10)
    loss = jnp.mean(optax.softmax_cross_entropy(logits, one_hot))
    return loss, logits
  grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
  (_, logits), grads = grad_fn(state.params)
  new_state = state.apply_gradients(grads=grads)
  metrics = compute_metrics(logits, batch['label'])


  return new_state, metrics
@functools.partial(jax.jit, static_argnums=2)
def train_step(state, batch, learning_rate_fn):
  def loss_fn(params):
    logits = CNN().apply({'params': params}, batch['image'])
    one_hot = jax.nn.one_hot(batch['label'], 10)
    loss = jnp.mean(optax.softmax_cross_entropy(logits, one_hot))
    return loss, logits
  grad_fn = jax.value_and_grad(loss_fn, has_aux=True)
  (_, logits), grads = grad_fn(state.params)
  new_state = state.apply_gradients(grads=grads)
  metrics = compute_metrics(logits, batch['label'])
  lr = learning_rate_fn(state.step)
  metrics['learning_rate'] = lr
  return new_state, metrics

And the train_epoch function:

Default learning rate

Learning rate schedule

def train_epoch(state, train_ds, batch_size, epoch, rng):
  """Trains for a single epoch."""
  train_ds_size = len(train_ds['image'])
  steps_per_epoch = train_ds_size // batch_size
  perms = jax.random.permutation(rng, len(train_ds['image']))
  perms = perms[:steps_per_epoch * batch_size]
  perms = perms.reshape((steps_per_epoch, batch_size))
  batch_metrics = []
  for perm in perms:
    batch = {k: v[perm, ...] for k, v in train_ds.items()}
    state, metrics = train_step(state, batch)
    batch_metrics.append(metrics)

  # compute mean of metrics across each batch in epoch.
  batch_metrics = jax.device_get(batch_metrics)
  epoch_metrics = {
      k: np.mean([metrics[k] for metrics in batch_metrics])
      for k in batch_metrics[0]}

  logging.info('train epoch: %d, loss: %.4f, accuracy: %.2f', epoch,
               epoch_metrics['loss'], epoch_metrics['accuracy'] * 100)

  return state, epoch_metrics
def train_epoch(state, train_ds, batch_size, epoch, learning_rate_fn, rng):
  """Trains for a single epoch."""
  train_ds_size = len(train_ds['image'])
  steps_per_epoch = train_ds_size // batch_size
  perms = jax.random.permutation(rng, len(train_ds['image']))
  perms = perms[:steps_per_epoch * batch_size]
  perms = perms.reshape((steps_per_epoch, batch_size))
  batch_metrics = []
  for perm in perms:
    batch = {k: v[perm, ...] for k, v in train_ds.items()}
    state, metrics = train_step(state, batch, learning_rate_fn)
    batch_metrics.append(metrics)

  # compute mean of metrics across each batch in epoch.
  batch_metrics = jax.device_get(batch_metrics)
  epoch_metrics = {
      k: np.mean([metrics[k] for metrics in batch_metrics])
      for k in batch_metrics[0]}

  logging.info('train epoch: %d, loss: %.4f, accuracy: %.2f', epoch,
               epoch_metrics['loss'], epoch_metrics['accuracy'] * 100)

  return state, epoch_metrics

And the create_train_state function:

Default learning rate

Learning rate schedule

def create_train_state(rng, config):
  """Creates initial `TrainState`."""
  cnn = CNN()
  params = cnn.init(rng, jnp.ones([1, 28, 28, 1]))['params']
  tx = optax.sgd(config.learning_rate, config.momentum)
  return train_state.TrainState.create(
      apply_fn=cnn.apply, params=params, tx=tx)
def create_train_state(rng, config, learning_rate_fn):
  """Creates initial `TrainState`."""
  cnn = CNN()
  params = cnn.init(rng, jnp.ones([1, 28, 28, 1]))['params']
  tx = optax.sgd(learning_rate_fn, config.momentum)
  return train_state.TrainState.create(
      apply_fn=cnn.apply, params=params, tx=tx)