mindspore.experimental.optim.Adadelta

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

Implements Adadelta algorithm.

\[\begin{split}\begin{aligned} &\rule{150mm}{0.4pt} \\ &\textbf{input} : \gamma \text{ (lr)}, \: \theta_0 \text{ (params)}, \: f(\theta) \text{ (objective)}, \: \rho \text{ (decay)}, \: \lambda \text{ (weight decay)} \\ &\textbf{initialize} : v_0 \leftarrow 0 \: \text{ (square avg)}, \: u_0 \leftarrow 0 \: \text{ (accumulate variables)} \\[-1.ex] &\rule{110mm}{0.4pt} \\ &\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\ &\hspace{5mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\ &\hspace{5mm}if \: \lambda \neq 0 \\ &\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\ &\hspace{5mm} v_t \leftarrow v_{t-1} \rho + g^2_t (1 - \rho) \\ &\hspace{5mm}\Delta x_t \leftarrow \frac{\sqrt{u_{t-1} + \epsilon }}{ \sqrt{v_t + \epsilon} }g_t \hspace{21mm} \\ &\hspace{5mm} u_t \leftarrow u_{t-1} \rho + \Delta x^2_t (1 - \rho) \\ &\hspace{5mm}\theta_t \leftarrow \theta_{t-1} - \gamma \Delta x_t \\ &\rule{110mm}{0.4pt} \\[-1.ex] &\bf{return} \: \theta_t \\[-1.ex] &\rule{110mm}{0.4pt} \\[-1.ex] \end{aligned}\end{split}\]

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