class Adagrad(learning_rate: float | Callable[[array], array], eps: float = 1e-08)#

The Adagrad optimizer [1].

Our Adagrad implementation follows the original paper. In detail,

[1]: Duchi, J., Hazan, E. and Singer, Y., 2011. Adaptive subgradient methods for online learning and stochastic optimization. JMLR 2011.

\[\begin{split}v_{t+1} &= v_t + g_t^2 \\ w_{t+1} &= w_t - \lambda \frac{g_t}{\sqrt{v_{t+1}} + \epsilon}\end{split}\]
  • learning_rate (float or callable) – The learning rate \(\lambda\).

  • eps (float, optional) – The term \(\epsilon\) added to the denominator to improve numerical stability. Default: 1e-8


__init__(learning_rate[, eps])

apply_single(gradient, parameter, state)

Performs the Adagrad parameter update and stores \(v\) in the optimizer state.

init_single(parameter, state)

Initialize optimizer state