The Adam optimizer can dynamically adjust the learning rate of each parameter using the first-order moment estimation and the second-order moment estimation of the gradient. The Adam algorithm is proposed in Adam: A Method for Stochastic Optimization.

The updating formulas are as follows,

$\begin{split}\begin{gather*} m_{t+1} = \beta_1 * m_{t} + (1 - \beta_1) * g \\ v_{t+1} = \beta_2 * v_{t} + (1 - \beta_2) * g * g \\ l = \alpha * \frac{\sqrt{1-\beta_2^t}}{1-\beta_1^t} \\ w_{t+1} = w_{t} - l * \frac{m_{t+1}}{\sqrt{v_{t+1}} + \epsilon} \end{gather*}\end{split}$

$$m$$ represents the 1st moment vector moment1, $$v$$ represents the 2nd moment vector moment2, $$g$$ represents gradients, $$l$$ represents scaling factor, $$\beta_1, \beta_2$$ represent beta1 and beta2, $$t$$ represents the current step while $$beta_1^t$$ and $$beta_2^t$$ represent beta1_power and beta2_power, $$\alpha$$ represents learning_rate, $$w$$ represents params, $$\epsilon$$ represents eps.

Note

The sparse strategy is applied while the SparseGatherV2 operator is used for forward network. If the sparse strategy wants to be executed on the host, set the target to the CPU. The sparse feature is under continuous development.

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.

Parameters
• 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 is 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: 1e-3.

• 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 current step.

• beta1 (float) – The exponential decay rate for the 1st moment estimations. Should be in range (0.0, 1.0). Default: 0.9.

• beta2 (float) – The exponential decay rate for the 2nd moment estimations. Should be in range (0.0, 1.0). Default: 0.999.

• eps (float) – Term added to the denominator to improve numerical stability. Should be greater than 0. Default: 1e-8.

• use_locking (bool) – Whether to enable a lock to protect the updating process of variable tensors. If true, updates of the w, m, and v tensors will be protected by a lock. If false, the result is unpredictable. Default: False.

• use_nesterov (bool) – Whether to use Nesterov Accelerated Gradient (NAG) algorithm to update the gradients. If true, update the gradients using NAG. If false, update the gradients without using NAG. Default: False.

• weight_decay (float) – Weight decay (L2 penalty). It must be equal to or greater than 0. Default: 0.0.

• 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.

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 element of parameters is neither Parameter nor dict.

• TypeError – If beta1, beta2, eps or loss_scale is not a float.

• TypeError – If weight_decay is neither float nor int.

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

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

• ValueError – If beta1, beta2 is not in range (0.0, 1.0).

• ValueError – If weight_decay is less than 0.

Supported Platforms:

Ascend GPU CPU

Examples

>>> from mindspore import nn, Model
>>>
>>> net = Net()
>>> #1) All parameters use the same learning rate and weight decay
>>>
>>> #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.Adam(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)

property target

The property is used to determine whether the parameter is updated on host or device. The input type is str and can only be ‘CPU’, ‘Ascend’ or ‘GPU’.