AveragedAdam

class viabel.AveragedAdam(learning_rate, *, beta1=0.9, jitter=1e-08, diagnostics=False, component_wise=True)

Averaged Adam 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:

beta1float optional

Gradient moving average hyper parameter. The default is 0.9

jitter: `float` optional

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

component_wise: `boolean` optional

Indicator for component-wise normalization of discent direction

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

__init__(learning_rate, *, beta1=0.9, 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 m, \(\nu\) and, k, the exponential moving average of gradient, squared gradient, and iteration respectively