mxnet.optimizer.ftrl

FTRL optimizer.

Classes

Ftrl([learning_rate, lamda1, beta, ...])

The Ftrl optimizer.

class mxnet.optimizer.ftrl.Ftrl(learning_rate=0.1, lamda1=0.01, beta=1.0, use_fused_step=True, **kwargs)

Bases: Optimizer

The Ftrl optimizer.

Referenced from Ad Click Prediction: a View from the Trenches, available at http://dl.acm.org/citation.cfm?id=2488200.

eta :

\[\eta_{t,i} = \frac{learningrate}{\beta+\sqrt{\sum_{s=1}^tg_{s,i}^2}}\]

The optimizer updates the weight by:

rescaled_grad = clip(grad * rescale_grad, clip_gradient)
z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate
n += rescaled_grad**2
w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1)

If the storage types of weight, state and grad are all row_sparse, sparse updates are applied by:

for row in grad.indices:
    rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient)
    z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate
    n[row] += rescaled_grad[row]**2
    w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1)

The sparse update only updates the z and n for the weights whose row_sparse gradient indices appear in the current batch, rather than updating it for all indices. Compared with the original update, it can provide large improvements in model training throughput for some applications. However, it provides slightly different semantics than the original update, and may lead to different empirical results.

For details of the update algorithm, see ftrl_update.

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

Parameters:

• learning_rate (float, default 0.1) – 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.

• lamda1 (float, default 0.01) – L1 regularization coefficient.

• beta (float, default 1.0) – Per-coordinate learning rate correlation parameter.

• 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)

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)

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)

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().