mindspore.nn.RMSProp

class mindspore.nn.RMSProp(*args, **kwargs)

Implements Root Mean Squared Propagation (RMSProp) algorithm.

Update params according to the RMSProp algorithm.

The equation is as follows:

\[s_{t+1} = \rho s_{t} + (1 - \rho)(\nabla Q_{i}(w))^2\]

\[m_{t+1} = \beta m_{t} + \frac{\eta} {\sqrt{s_{t+1} + \epsilon}} \nabla Q_{i}(w)\]

\[w = w - m_{t+1}\]

The first equation calculates moving average of the squared gradient for each weight. Then dividing the gradient by \(\sqrt{ms_{t+1} + \epsilon}\).

if centered is True:

\[g_{t+1} = \rho g_{t} + (1 - \rho)\nabla Q_{i}(w)\]

\[s_{t+1} = \rho s_{t} + (1 - \rho)(\nabla Q_{i}(w))^2\]

\[m_{t+1} = \beta m_{t} + \frac{\eta} {\sqrt{s_{t+1} - g_{t+1}^2 + \epsilon}} \nabla Q_{i}(w)\]

\[w = w - m_{t+1}\]

where \(w\) represents params, which will be updated. \(g_{t+1}\) is mean gradients, \(g_{t}\) is the last moment of \(g_{t+1}\). \(s_{t+1}\) is the mean square gradients, \(s_{t}\) is the last moment of \(s_{t+1}\), \(m_{t+1}\) is moment, the delta of w, \(m_{t}\) is the last moment of \(m_{t+1}\). \(\rho\) represents decay. \(\beta\) is the momentum term, represents momentum. \(\epsilon\) is a smoothing term to avoid division by zero, represents epsilon. \(\eta\) is learning rate, represents learning_rate. \(\nabla Q_{i}(w)\) is gradients, represents gradients.

Note

When separating parameter groups, the weight decay in each group will be applied on the parameters if the weight decay is positive. When not separating parameter groups, the weight_decay in the API will be applied on the parameters without ‘beta’ or ‘gamma’ in their names if weight_decay is positive.

When separating parameter groups, if you want to centralize the gradient, set grad_centralization to True, but the gradient centralization can only be applied to the parameters of the convolution layer. If the parameters of the non convolution layer are set to True, an error will be reported.

To improve parameter groups performance, the customized order of parameters can be supported.

Parameters

• params (Union[list[Parameter], list[dict]]) –

  When the params is a list of Parameter which will be updated, the element in params must be class Parameter. When the params is a list of dict, the “params”, “lr”, “weight_decay” and “order_params” are the keys can be parsed.

  • params: Required. The value must be a list of Parameter.

  • lr: Optional. If “lr” in the keys, the value of corresponding learning rate will be used. If not, the learning_rate in the API will be used.

  • weight_decay: Optional. If “weight_decay” in the keys, the value of corresponding weight decay will be used. If not, the weight_decay in the API will be used.

  • order_params: Optional. If “order_params” in the keys, the value must be the order of parameters and the order will be followed in optimizer. There are no other keys in the dict and the parameters which in the value of ‘order_params’ must be in one of group parameters.

  • grad_centralization: Optional. The data type of “grad_centralization” is Bool. If “grad_centralization” is in the keys, the set value will be used. If not, the grad_centralization is False by default. This parameter only works on the convolution layer.

• learning_rate (Union[float, Tensor, Iterable, LearningRateSchedule]) – A value or a graph for the learning rate. When the learning_rate is an Iterable or a Tensor in a 1D dimension, use dynamic learning rate, then the i-th step will take the i-th value as the learning rate. When the learning_rate is LearningRateSchedule, use dynamic learning rate, the i-th learning rate will be calculated during the process of training according to the formula of LearningRateSchedule. When the learning_rate is a float or a Tensor in a zero dimension, use fixed learning rate. Other cases are not supported. The float learning rate must be equal to or greater than 0. If the type of learning_rate is int, it will be converted to float. Default: 0.1.

• decay (float) – Decay rate. Should be equal to or greater than 0. Default: 0.9.

• momentum (float) – Hyperparameter of type float, means momentum for the moving average. Should be equal to or greater than 0. Default: 0.0.

• epsilon (float) – Term added to the denominator to improve numerical stability. Should be greater than 0. Default: 1e-10.

• use_locking (bool) – Whether to enable a lock to protect the variable and accumlation tensors from being updated. Default: False.

• centered (bool) – If true, gradients are normalized by the estimated variance of the gradient. Default: False.

• loss_scale (float) – A floating point value for the loss scale. Should be greater than 0. In general, use the default value. Only when FixedLossScaleManager is used for training and the drop_overflow_update in FixedLossScaleManager is set to False, then this value needs to be the same as the loss_scale in FixedLossScaleManager. Refer to class mindspore.FixedLossScaleManager for more details. Default: 1.0.

• weight_decay (Union[float, int]) – Weight decay (L2 penalty). Should be equal to or greater than 0. Default: 0.0.

Inputs:

• gradients (tuple[Tensor]) - The gradients of params, the shape is the same as params.

Outputs:

Tensor[bool], the value is True.

Raises

• TypeError – If learning_rate is not one of int, float, Tensor, Iterable, LearningRateSchedule.

• TypeError – If decay, momentum, epsilon or loss_scale is not a float.

• TypeError – If element of parameters is neither Parameter nor dict.

• TypeError – If weight_decay is neither float nor int.

• TypeError – If use_locking or centered is not a bool.

• ValueError – If epsilon is less than or equal to 0.

• ValueError – If decay or momentum is less than 0.

Supported Platforms:

Ascend GPU CPU

Examples

>>> net = Net()
>>> #1) All parameters use the same learning rate and weight decay
>>> optim = nn.RMSProp(params=net.trainable_params(), learning_rate=0.1)
>>>
>>> #2) Use parameter groups and set different values
>>> conv_params = list(filter(lambda x: 'conv' in x.name, net.trainable_params()))
>>> no_conv_params = list(filter(lambda x: 'conv' not in x.name, net.trainable_params()))
>>> group_params = [{'params': conv_params, 'weight_decay': 0.01, 'grad_centralization':True},
...                 {'params': no_conv_params, 'lr': 0.01},
...                 {'order_params': net.trainable_params()}]
>>> optim = nn.RMSProp(group_params, learning_rate=0.1, weight_decay=0.0)
>>> # The conv_params's parameters will use default learning rate of 0.1 and weight decay of 0.01 and grad
>>> # centralization of True.
>>> # The no_conv_params's parameters will use learning rate of 0.01 and default weight decay of 0.0 and grad
>>> # centralization of False.
>>> # The final parameters order in which the optimizer will be followed is the value of 'order_params'.
>>>
>>> loss = nn.SoftmaxCrossEntropyWithLogits()
>>> model = Model(net, loss_fn=loss, optimizer=optim)