class paddle.fluid.optimizer.AdamaxOptimizer(learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-08, regularization=None, name=None)[source]

The Adamax optimizer is implemented based on the Adamax Optimization in Section 7 of Adam paper. The Adamax algorithm is a variant of the Adam algorithm based on the infinite norm, which makes the learning rate update algorithm more stable and simple.

The parameter param_out update rule with gradient grad:

\[ \begin{align}\begin{aligned}t & = t + 1\\moment\_out & = {\beta}_1 * moment + (1 - {\beta}_1) * grad\\inf\_norm\_out & = max({\beta}_2 * inf\_norm + \epsilon, |grad|)\\learning\_rate & = \frac{learning\_rate}{1 - {\beta}_1^t}\\param\_out & = param - learning\_rate * \frac{moment\_out}{inf\_norm\_out}\end{aligned}\end{align} \]

Related paper: Adam: A Method for Stochastic Optimization

The original paper does not have an epsilon attribute, it is added here for numerical stability to prevent the division by 0 error.

  • learning_rate (float|Variable, optional) – The learning rate used to update Parameter. It can be a float value or a Variable with a float type. The default value is 0.001.

  • beta1 (float, optional) – The exponential decay rate for the 1st moment estimates. The default value is 0.9.

  • beta2 (float, optional) – The exponential decay rate for the 2nd moment estimates. The default value is 0.999.

  • epsilon (float, optional) – A small float value for numerical stability. The default value is 1e-08.

  • regularization (WeightDecayRegularizer, optional) – A Regularizer, such as L2DecayRegularizer. The default value is None.

  • name (str, optional) – Normally there is no need for user to set this property. For more information, please refer to Name. The default value is None.


Currently, AdamaxOptimizer doesn’t support sparse parameter optimization.


import paddle.fluid as fluid
import numpy

# First create the Executor.
place = fluid.CPUPlace() # fluid.CUDAPlace(0)
exe = fluid.Executor(place)

train_program = fluid.Program()
startup_program = fluid.Program()
with fluid.program_guard(train_program, startup_program):
    data ='X', shape=[None, 1], dtype='float32')
    hidden = fluid.layers.fc(input=data, size=10)
    loss = fluid.layers.mean(hidden)
    adam = fluid.optimizer.AdamaxOptimizer(learning_rate=0.2)

# Run the startup program once and only once.

x = numpy.random.random(size=(10, 1)).astype('float32')
outs =,
              feed={'X': x},
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()