netket.optimizer.AdaGrad

netket.optimizer.AdaGrad(learning_rate=0.001, epscut=1e-07, initial_accumulator_value=0.1)

AdaGrad Optimizer. In many cases, in Sgd the learning rate \(\eta\) should decay as a function of training iteration to prevent overshooting as the optimum is approached. AdaGrad is an adaptive learning rate algorithm that automatically scales the learning rate with a sum over past gradients. The vector \(\mathbf{g}\) is initialized to zero. Given a stochastic estimate of the gradient of the cost function \(G(\mathbf{p})\), the updates for \(g_k\) and the parameter \(p_k\) are

\[\begin{split}g^\prime_k &= g_k + G_k(\mathbf{p})^2\\ p^\prime_k &= p_k - \frac{\eta}{\sqrt{g_k + \epsilon}}G_k(\mathbf{p})\end{split}\]

AdaGrad has been shown to perform particularly well when the gradients are sparse, but the learning rate may become too small after many updates because the sum over the squares of past gradients is cumulative.

Parameters:

• learning_rate (float) – Learning rate \(\eta\).

• epscut (float) – Small \(\epsilon\) cutoff.

• initial_accumulator_value (float) – initial value of the accumulator

Examples

Simple AdaGrad optimizer.

>>> from netket.optimizer import AdaGrad
>>> op = AdaGrad()