AveragedRMSProp

class viabel.AveragedRMSProp(learning_rate, *, jitter=1e-08, diagnostics=False, component_wise=True)

Averaged RMSProp optimization method (Mukkamala and Hein, 2017, §4)

Uses averaged squared gradient by setting \(\beta_k = 1-1/k\) such that

\[\nu^{(k+1)} = \beta_k \nu^{(k)} + (1-\beta_k) \hat{g}^{(k)} \cdot \hat{g}^{(k)}.\]

Then,

\[\nu^{(k+1)} = (k+1)^{-1} \sum^k_{k^\prime =0}\hat{g}^{(k)} \cdot \hat{g}^{(k)},\]

where \(\nu^{(k)}\) converges to a constant almost surely under certain conditions.

Parameters:

jitter: `float` optional

Small value used for numerical stability. The default is 1e-8

component_wise: `boolean` optional

Indication of component wise discent direction computation

Returns:

descent_dirnumpy.ndarray, shape(var_param_dim,)

Descent direction of the optimization algorithm

Methods

descent_direction(grad)	Compute descent direction for optimization.
optimize(n_iters, objective, init_param[, ...])	Parameters:
reset_state()	resetting \(\nu\) and k, the exponential moving average of squared gradient and iteration respectively

__init__(learning_rate, *, jitter=1e-08, diagnostics=False, component_wise=True)

Parameters:

learning_ratefloat

Tuning parameter that determines the step size

weight_decay: `float`

L2 regularization weight

iterate_avg_propfloat

Proportion of iterates to use for computing iterate average. None means no iterate averaging. The default is 0.2.

diagnosticsbool, optional

Record diagnostic information if True. The default is False.

descent_direction(grad)

Compute descent direction for optimization.

Default implementation returns grad.

Parameters:

gradnumpy.ndarray, shape(var_param_dim,)

(stochastic) gradient of the objective function

Returns:

descent_dirnumpy.ndarray, shape(var_param_dim,)

Descent direction of the optimization algorithm

reset_state()

resetting \(\nu\) and k, the exponential moving average of squared gradient and iteration respectively