class paddle.fluid.optimizer.RMSPropOptimizer(learning_rate, rho=0.95, epsilon=1e-06, momentum=0.0, centered=False, regularization=None, name=None)[source]

Root Mean Squared Propagation (RMSProp) is an unpublished, adaptive learning rate method. The original slides proposed RMSProp: Slide 29 of http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf .

The original equation is as follows:

\[ \begin{align}\begin{aligned}r(w, t) & = \rho r(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2\\w & = w - \frac{\eta} {\sqrt{r(w,t) + \epsilon}} \nabla Q_{i}(w)\end{aligned}\end{align} \]

The first equation calculates moving average of the squared gradient for each weight. Then dividing the gradient by \(sqrt{v(w,t)}\).

In some cases, adding a momentum term :math: beta is beneficial. In our implementation, Nesterov momentum is used:

\[ \begin{align}\begin{aligned}r(w, t) & = \rho r(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2\\v(w, t) & = \beta v(w, t-1) + \frac{\eta} {\sqrt{r(w,t) + \epsilon}} \nabla Q_{i}(w)\\w & = w - v(w, t)\end{aligned}\end{align} \]

if centered is True:

\[ \begin{align}\begin{aligned}r(w, t) & = \rho r(w, t-1) + (1 - \rho)(\nabla Q_{i}(w))^2\\g(w, t) & = \rho g(w, t-1) + (1 - \rho)\nabla Q_{i}(w)\\v(w, t) & = \beta v(w, t-1) + \frac{\eta} {\sqrt{r(w,t) - (g(w, t))^2 + \epsilon}} \nabla Q_{i}(w)\\w & = w - v(w, t)\end{aligned}\end{align} \]

where, \(\rho\) is a hyperparameter and typical values are 0.9, 0.95 and so on. :math: beta is the momentum term. :math: epsilon is a smoothing term to avoid division by zero, usually set somewhere in range from 1e-4 to 1e-8.

  • learning_rate (float) – Global learning rate.

  • rho (float) – rho is :math: rho in equation, default is 0.95.

  • epsilon (float) –


    epsilon in equation is smoothing term to

    avoid division by zero, default is 1e-6.

  • momentum (float) – \(\beta\) in equation is the momentum term, default is 0.0.

  • centered (bool) – If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False.

  • regularization – A Regularizer, such as L2DecayRegularizer. Optional, default is None.

  • name (str, optional) – This parameter is used by developers to print debugging information. For details, please refer to Name. Default is None.


ValueError – If learning_rate, rho, epsilon, momentum are None.


import paddle
import paddle.fluid as fluid
import numpy as np

place = fluid.CPUPlace()
main = fluid.Program()
with fluid.program_guard(main):
    x = fluid.layers.data(name='x', shape=[13], dtype='float32')
    y = fluid.layers.data(name='y', shape=[1], dtype='float32')
    y_predict = fluid.layers.fc(input=x, size=1, act=None)
    cost = fluid.layers.square_error_cost(input=y_predict, label=y)
    avg_cost = fluid.layers.mean(cost)

    rms_optimizer = fluid.optimizer.RMSProp(learning_rate=0.1)

    fetch_list = [avg_cost]
    train_reader = paddle.batch(
        paddle.dataset.uci_housing.train(), batch_size=1)
    feeder = fluid.DataFeeder(place=place, feed_list=[x, y])
    exe = fluid.Executor(place)
    for data in train_reader():
        exe.run(main, feed=feeder.feed(data), fetch_list=fetch_list)
minimize(loss, startup_program=None, parameter_list=None, no_grad_set=None, grad_clip=None)

Add operations to minimize loss by updating parameter_list.

  • loss (Variable) – A Variable containing the value to minimize.

  • startup_program (Program, optional) – Program for initializing parameters in parameter_list. The default value is None, at this time default_startup_program will be used.

  • parameter_list (list, optional) – List of Variable names to update to minimize loss. The default value is None, at this time all parameters will be updated.

  • no_grad_set (set, optional) – Set of Variable objects that don’t need to be updated. The default value is None.

  • grad_clip (GradClipBase, optional) – Gradient clipping strategy, static graph mode does not need to use this argument. Currently, this argument only supports gradient clipping in dygraph mode. In the future, this argument my be adjusted. The default value is None.


tuple (optimize_ops, params_grads), A list of operators appended by minimize and a list of (param, grad) variable pairs, param is Parameter, grad is the gradient value corresponding to the parameter.

Return type



Please refer to the example of current Optimizer.


Load optimizer state dict. For Adam opimizer, contains beta1, beta2, momentum etc. If LearningRateDecay have been used, global_step will be changed.


state_dict (dict) – Dict contains all the Variable needed by optimizer




with fluid.dygraph.guard():
    emb = fluid.dygraph.Embedding( "emb", [10, 10])

    state_dict = emb.state_dict()
    fluid.save_dygraph( state_dict, "paddle_dy")

    adam = fluid.optimizer.Adam( learning_rate = fluid.layers.noam_decay( 100, 10000) )
    state_dict = adam.state_dict()
    fluid.save_dygraph( state_dict, "padle_dy")

    para_state_dict, opti_state_dict = fluid.load_dygraph( "paddle_dy")

    adam.set_dict( opti_state_dict )

Get state dict information from optimizer. It contain all the variable used by optimizer. For Adam opimizer, contains beta1, beta2, momentum etc. If LearningRateDecay have been used, global_step will be include in state dict. If the optimzier never be called(minimize function), the state_dict is empty.

Args: None :returns: dict contains all the variablel used by optimizer :rtype: state_dict(dict)


import paddle.fluid as fluid
adam = fluid.optimizer.Adam(0.001)
state_dict = adam.state_dict()