SGD

[source]

SGD class

tf.keras.optimizers.SGD(
    learning_rate=0.01, momentum=0.0, nesterov=False, name="SGD", **kwargs
)

Gradient descent (with momentum) optimizer.

Update rule for parameter w with gradient g when momentum is 0:

w = w - learning_rate * g

Update rule when momentum is larger than 0:

velocity = momentum * velocity - learning_rate * g
w = w + velocity

When nesterov=True, this rule becomes:

velocity = momentum * velocity - learning_rate * g
w = w + momentum * velocity - learning_rate * g

Arguments

  • learning_rate: A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.01.
  • momentum: float hyperparameter >= 0 that accelerates gradient descent in the relevant direction and dampens oscillations. Defaults to 0, i.e., vanilla gradient descent.
  • nesterov: boolean. Whether to apply Nesterov momentum. Defaults to False.
  • name: Optional name prefix for the operations created when applying gradients. Defaults to "SGD".
  • **kwargs: keyword arguments. Allowed arguments are clipvalue, clipnorm, global_clipnorm. If clipvalue (float) is set, the gradient of each weight is clipped to be no higher than this value. If clipnorm (float) is set, the gradient of each weight is individually clipped so that its norm is no higher than this value. If global_clipnorm (float) is set the gradient of all weights is clipped so that their global norm is no higher than this value.

Usage:

>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1)
>>> var = tf.Variable(1.0)
>>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> # Step is `- learning_rate * grad`
>>> var.numpy()
0.9
>>> opt = tf.keras.optimizers.SGD(learning_rate=0.1, momentum=0.9)
>>> var = tf.Variable(1.0)
>>> val0 = var.value()
>>> loss = lambda: (var ** 2)/2.0         # d(loss)/d(var1) = var1
>>> # First step is `- learning_rate * grad`
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val1 = var.value()
>>> (val0 - val1).numpy()
0.1
>>> # On later steps, step-size increases because of momentum
>>> step_count = opt.minimize(loss, [var]).numpy()
>>> val2 = var.value()
>>> (val1 - val2).numpy()
0.18

Reference