mxnet.optimizer.signum

Signum optimizer.

Classes

Signum([learning_rate, momentum, wd_lh, ...])

The Signum optimizer that takes the sign of gradient or momentum.
class mxnet.optimizer.signum.Signum(learning_rate=0.01, momentum=0.9, wd_lh=0.0, use_fused_step=True, **kwargs)[source]

Bases: Optimizer

The Signum optimizer that takes the sign of gradient or momentum.

The optimizer updates the weight by:

rescaled_grad = rescale_grad * clip(grad, clip_gradient) + wd * weight
state = momentum * state + (1-momentum)*rescaled_grad
weight = (1 - lr * wd_lh) * weight - lr * sign(state)

References

Jeremy Bernstein, Yu-Xiang Wang, Kamyar Azizzadenesheli & Anima Anandkumar. (2018). signSGD: Compressed Optimisation for Non-Convex Problems. In ICML’18.

See: https://arxiv.org/abs/1802.04434

For details of the update algorithm see signsgd_update and signum_update.

This optimizer accepts the following parameters in addition to those accepted by Optimizer.

Parameters:

  • learning_rate (float, default 0.01) – The initial learning rate. If None, the optimization will use the learning rate from lr_scheduler. If not None, it will overwrite the learning rate in lr_scheduler. If None and lr_scheduler is also None, then it will be set to 0.01 by default.

  • momentum (float, optional) – The momentum value.

  • wd_lh (float, optional) – The amount of decoupled weight decay regularization, see details in the original paper at:https://arxiv.org/abs/1711.05101

  • use_fused_step (bool, default True) – Whether or not to use fused kernels for optimizer. When use_fused_step=False, step is called, otherwise, fused_step is called.

create_state(index, weight)[source]

Creates auxiliary state for a given weight.

Some optimizers require additional states, e.g. as momentum, in addition to gradients in order to update weights. This function creates state for a given weight which will be used in update. This function is called only once for each weight.

Parameters:

  • index (int) – An unique index to identify the weight.

  • weight (NDArray) – The weight.

Returns:

state – The state associated with the weight.

Return type:

any obj

fused_step(indices, weights, grads, states)[source]

Perform a fused optimization step using gradients and states. Fused kernel is used for update.

Parameters:

  • indices (list of int) – List of unique indices of the parameters into the individual learning rates and weight decays. Learning rates and weight decay may be set via set_lr_mult() and set_wd_mult(), respectively.

  • weights (list of NDArray) – List of parameters to be updated.

  • grads (list of NDArray) – List of gradients of the objective with respect to this parameter.

  • states (List of any obj) – List of state returned by create_state().

step(indices, weights, grads, states)[source]

Perform an optimization step using gradients and states.

Parameters:

  • indices (list of int) – List of unique indices of the parameters into the individual learning rates and weight decays. Learning rates and weight decay may be set via set_lr_mult() and set_wd_mult(), respectively.

  • weights (list of NDArray) – List of parameters to be updated.

  • grads (list of NDArray) – List of gradients of the objective with respect to this parameter.

  • states (List of any obj) – List of state returned by create_state().