class mindspore.nn.RMSProp(*args, **kwargs)[source]

Implements Root Mean Squared Propagation (RMSProp) algorithm.

Update params according to the RMSProp algorithm. The 29th of the original presentation slide [http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf] proposes RMSProp. 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. \(s_{t+1}\) is the mean square gradients. \(m_{t+1}\) is moment, the delta of w. \(\rho\) 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. \(t\) represents the current step.


If parameters are not grouped, the weight_decay in optimizer will be applied on the network parameters without ‘beta’ or ‘gamma’ in their names. Users can group parameters to change the strategy of decaying weight. When parameters are grouped, each group can set weight_decay, if not, the weight_decay in optimizer will be applied.

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

    Must be list of Parameter or list of dict. When the params is a list of dict, the string “params”, “lr”, “weight_decay”, “grad_centralization” and “order_params” are the keys can be parsed.

    • params: Required. Parameters in current group. 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 optimizer will be used. Fixed and dynamic learning rate are supported.

    • 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 optimizer will be used.

    • grad_centralization: Optional. Must be Boolean. If “grad_centralization” is in the keys, the set value will be used. If not, the grad_centralization is False by default. This configuration only works on the convolution layer.

    • order_params: Optional. When parameters are grouped, this usually is used to maintain the order of parameters that appeared in the network to improve performance. The value should be parameters whose order will be followed in optimizer. If order_params in the keys, other keys will be ignored and the element of ‘order_params’ must be in one group of params.

  • learning_rate (Union[float, int, Tensor, Iterable, LearningRateSchedule]) –

    Default: 0.1.

    • float: The fixed learning rate value. Must be equal to or greater than 0.

    • int: The fixed learning rate value. Must be equal to or greater than 0. It will be converted to float.

    • Tensor: Its value should be a scalar or a 1-D vector. For scalar, fixed learning rate will be applied. For vector, learning rate is dynamic, then the i-th step will take the i-th value as the learning rate.

    • Iterable: Learning rate is dynamic. The i-th step will take the i-th value as the learning rate.

    • LearningRateSchedule: Learning rate is dynamic. During training, the optimizer calls the instance of LearningRateSchedule with step as the input to get the learning rate of the current step.

  • 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 updating process of variable tensors. 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.

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


Tensor[bool], the value is True.

  • 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


>>> from mindspore import nn, Model
>>> 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)