mindspore.experimental.optim.Adadelta

class mindspore.experimental.optim.Adadelta(params, lr=1.0, rho=0.9, eps=1e-6, weight_decay=0.0, *, maximize=False)

Implements Adadelta algorithm.

\[ \begin{align}\begin{aligned}\newcommand{\grad}[2]{\nabla_{#1} f_{#2}(#2_{#2 - 1})} \newcommand{\updateVar}[3]{#1_{#2} \leftarrow #1_{#2 - 1} \rho + #3_{#2} (1 - \rho)}\\\begin{split}\begin{align*} &\rule{150mm}{0.4pt} \\ &\textbf{Input}: \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}, \: \rho \text{ (decay)}, \: \lambda \text{ (weight decay)} \\ &\textbf{Initialize}: \begin{cases} v_0 \leftarrow 0 \text{ (square avg)} \\ u_0 \leftarrow 0 \text{ (accumulate variables)} \end{cases} \\ &\rule{110mm}{0.4pt} \\ &\textbf{For } t = 1 \text{ to } \ldots \text{ do}: \\ &\quad g_t \leftarrow \grad{\theta}{t} \\ &\quad \text{If } \lambda \neq 0: \\ &\quad\quad g_t \leftarrow g_t + \lambda \theta_{t - 1} \\ &\quad v_t \leftarrow \updateVar{v}{t}{g^2} \\ &\quad \Delta x_t \leftarrow \frac{\sqrt{u_{t - 1} + \epsilon}}{\sqrt{v_t + \epsilon}} g_t \\ &\quad u_t \leftarrow \updateVar{u}{t}{\Delta x^2} \\ &\quad \theta_t \leftarrow \theta_{t - 1} - \gamma \Delta x_t \\ &\rule{110mm}{0.4pt} \\ &\bf{Return}: \theta_t \\ &\rule{110mm}{0.4pt} \end{align*}\end{split}\end{aligned}\end{align} \]

Warning

This is an experimental optimizer API that is subject to change. This module must be used with lr scheduler module in LRScheduler Class .

Parameters

• params (Union[list(Parameter), list(dict)]) – list of parameters to optimize or dicts defining parameter groups.

• lr (Union[int, float, Tensor], optional) – learning rate. Default: 1.0.

• rho (float, optional) – coefficient used for computing a running average of squared gradients. \(\rho\) in the formula above. Default: 0.9.

• eps (float, optional) – term added to the denominator to improve numerical stability. \(\epsilon\) in the formula above. Default: 1e-6.

• weight_decay (float, optional) – weight decay (L2 penalty). Default: 0..

Keyword Arguments

maximize (bool, optional) – maximize the params based on the objective, instead of minimizing. Default: False.

Inputs:

• gradients (tuple[Tensor]) - The gradients of params.

Raises

• ValueError – If the learning rate is not int, float or Tensor.

• ValueError – If the learning rate is less than 0.

• ValueError – If the eps is less than or equal to 0.0.

• ValueError – If the rho is not in the range of [0, 1].

• ValueError – If the weight_decay is less than 0.

Supported Platforms:

Ascend GPU CPU

Examples

>>> import mindspore
>>> from mindspore import nn
>>> from mindspore.experimental import optim
>>> # Define the network structure of LeNet5. Refer to
>>> # https://gitee.com/mindspore/docs/blob/master/docs/mindspore/code/lenet.py
>>> net = LeNet5()
>>> loss_fn = nn.SoftmaxCrossEntropyWithLogits(sparse=True)
>>> optimizer = optim.Adadelta(net.trainable_params(), lr=0.1)
>>> def forward_fn(data, label):
...     logits = net(data)
...     loss = loss_fn(logits, label)
...     return loss, logits
>>> grad_fn = mindspore.value_and_grad(forward_fn, None, optimizer.parameters, has_aux=True)
>>> def train_step(data, label):
...     (loss, _), grads = grad_fn(data, label)
...     optimizer(grads)
...     return loss