tf.keras.optimizers.Adamax

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Optimizer that implements the Adamax algorithm.

Inherits From: Optimizer

tf.keras.optimizers.Adamax(
    learning_rate=0.001,
    beta_1=0.9,
    beta_2=0.999,
    epsilon=1e-07,
    name='Adamax',
    **kwargs
)

It is a variant of Adam based on the infinity norm. Default parameters follow those provided in the paper. Adamax is sometimes superior to adam, specially in models with embeddings.

Initialization:

m = 0  # Initialize initial 1st moment vector
v = 0  # Initialize the exponentially weighted infinity norm
t = 0  # Initialize timestep

The update rule for parameter w with gradient g is described at the end of section 7.1 of the paper:

t += 1
m = beta1 * m + (1 - beta) * g
v = max(beta2 * v, abs(g))
current_lr = learning_rate / (1 - beta1 ** t)
w = w - current_lr * m / (v + epsilon)

Similarly to Adam, the epsilon is added for numerical stability (especially to get rid of division by zero when v_t == 0).

In contrast to Adam, the sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) only updates variable slices and corresponding m_t, v_t terms when that part of the variable was used in the forward pass. This means that the sparse behavior is contrast to the dense behavior (similar to some momentum implementations which ignore momentum unless a variable slice was actually used).