mlx.optimizers.AdamW#

class AdamW(learning_rate: float | Callable[[array], array], betas: List[float] = [0.9, 0.999], eps: float = 1e-08, weight_decay: float = 0.01)#

The AdamW optimizer [1].

Following the above convention, in contrast with [1], we do not use bias correction in the first and second moments for AdamW. We update the weights with a weight_decay (\(\lambda\)) value:

[1]: Loshchilov, I. and Hutter, F., 2019. Decoupled weight decay regularization. ICLR 2019.

\[\begin{split}m_{t+1} &= \beta_1 m_t + (1 - \beta_1) g_t \\ v_{t+1} &= \beta_2 v_t + (1 - \beta_2) g_t^2 \\ w_{t+1} &= w_t - \alpha (\frac{m_{t+1}}{\sqrt{v_{t+1} + \epsilon}} + \lambda w_t)\end{split}\]
Parameters:

  • learning_rate (float or callable) – The learning rate \(\alpha\).

  • betas (Tuple[float, float], optional) – The coefficients \((\beta_1, \beta_2)\) used for computing running averages of the gradient and its square. Default: (0.9, 0.999)

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

  • weight_decay (float, optional) – The weight decay \(\lambda\). Default: 0.

Methods

__init__(learning_rate[, betas, eps, ...])

apply_single(gradient, parameter, state)

Performs the AdamW parameter update by modifying the parameters passed into Adam.