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# ============================================================================
"""adam"""
from __future__ import absolute_import
from mindspore.ops import functional as F, operations as P
from mindspore.common.parameter import Parameter, ParameterTuple
from mindspore.common.tensor import Tensor
import mindspore.common.dtype as mstype
from mindspore.nn.optim_ex.optimizer import Optimizer
from mindspore import ops
[文档]class Adam(Optimizer):
r"""
Implements Adam algorithm..
The updating formulas are as follows:
.. math::
\begin{aligned}
&\textbf{input} : \gamma \text{ (lr)}, \beta_1, \beta_2
\text{ (betas)},\theta_0 \text{ (params)},f(\theta) \text{ (objective)} \\
&\hspace{13mm} \lambda \text{ (weight decay)}, \: \textit{amsgrad},
\:\textit{maximize} \\
&\textbf{initialize} : m_0 \leftarrow 0 \text{ ( first moment)},
v_0\leftarrow 0 \text{ (second moment)},\: \widehat{v_0}^{max}\leftarrow 0\\[-1.ex]
&\textbf{for} \: t=1 \: \textbf{to} \: \ldots \: \textbf{do} \\
&\hspace{5mm}\textbf{if} \: \textit{maximize}: \\
&\hspace{10mm}g_t \leftarrow -\nabla_{\theta} f_t (\theta_{t-1}) \\
&\hspace{5mm}\textbf{else} \\
&\hspace{10mm}g_t \leftarrow \nabla_{\theta} f_t (\theta_{t-1}) \\
&\hspace{5mm}\textbf{if} \: \lambda \neq 0 \\
&\hspace{10mm} g_t \leftarrow g_t + \lambda \theta_{t-1} \\
&\hspace{5mm}m_t \leftarrow \beta_1 m_{t-1} + (1 - \beta_1) g_t \\
&\hspace{5mm}v_t \leftarrow \beta_2 v_{t-1} + (1-\beta_2) g^2_t \\
&\hspace{5mm}\widehat{m_t} \leftarrow m_t/\big(1-\beta_1^t \big) \\
&\hspace{5mm}\widehat{v_t} \leftarrow v_t/\big(1-\beta_2^t \big) \\
&\hspace{5mm}\textbf{if} \: amsgrad \\
&\hspace{10mm}\widehat{v_t}^{max} \leftarrow \mathrm{max}(\widehat{v_t}^{max},
\widehat{v_t}) \\
&\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
\big(\sqrt{\widehat{v_t}^{max}} + \epsilon \big) \\
&\hspace{5mm}\textbf{else} \\
&\hspace{10mm}\theta_t \leftarrow \theta_{t-1} - \gamma \widehat{m_t}/
\big(\sqrt{\widehat{v_t}} + \epsilon \big) \\
&\bf{return} \: \theta_t \\[-1.ex]
\end{aligned}
.. warning::
This is an experimental optimizer API that is subject to change.
This module must be used with lr scheduler module in `LRScheduler Class
<https://www.mindspore.cn/docs/en/r2.1/api_python/mindspore.nn.html#lrscheduler-class>`_ .
Args:
params (Union[list(Parameter), list(dict)]): list of parameters to optimize or dicts defining
parameter groups
lr (Union[int, float, Tensor], optional): learning rate. Default: ``1e-3``.
betas (Tuple[float, float], optional): The exponential decay rate for the moment estimations.
Default: ``(0.9, 0.999)``.
eps (float, optional): term added to the denominator to improve
numerical stability. Default: ``1e-8``.
weight_decay (float, optional): weight decay (L2 penalty). Default: ``0``.
amsgrad (bool, optional): whether to use the AMSGrad algorithm. Default: ``False``.
Keyword Args:
maximize (bool, optional): maximize the params based on the objective, instead of minimizing.
Default: ``False``.
Inputs:
- **gradients** (tuple[Tensor]) - The gradients of `params`.
Raises:
ValueError: If the `lr` is not int, float or Tensor.
ValueError: If the `lr` is less than 0.
ValueError: If the `eps` is less than 0.0.
ValueError: If the `betas` not in the range of 0-1.
ValueError: If the `weight_decay` is less than 0.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> import mindspore
>>> from mindspore import nn
>>> # Define the network structure of LeNet5. Refer to
>>> # https://gitee.com/mindspore/docs/blob/r2.1/docs/mindspore/code/lenet.py
>>> net = LeNet5()
>>> loss_fn = nn.SoftmaxCrossEntropyWithLogits(sparse=True)
>>> optimizer = nn.optim_ex.Adam(net.trainable_params(), lr=0.1)
>>> def forward_fn(data, label):
... logits = net(data)
... loss = loss_fn(logits, label)
... return loss, logits
>>> grad_fn = mindspore.value_and_grad(forward_fn, None, optimizer.parameters, has_aux=True)
>>> def train_step(data, label):
... (loss, _), grads = grad_fn(data, label)
... optimizer(grads)
... return loss
"""
def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
weight_decay=0, amsgrad=False, *, maximize=False):
if lr < 0.0:
raise ValueError("Invalid learning rate: {}".format(lr))
if eps < 0.0:
raise ValueError("Invalid epsilon value: {}".format(eps))
if not 0.0 <= betas[0] < 1.0:
raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
if not 0.0 <= betas[1] < 1.0:
raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
if weight_decay < 0.0:
raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
defaults = dict(lr=lr, betas=betas, eps=eps,
weight_decay=weight_decay, amsgrad=amsgrad,
maximize=maximize)
super(Adam, self).__init__(params, defaults)
self.exp_avg = self.parameters.clone(prefix="exp_avg", init='zeros')
self.exp_avg_sq = self.parameters.clone(prefix="exp_avg_sq", init='zeros')
self.max_exp_avg_sq = self.parameters.clone(prefix="max_exp_avg_sq", init='zeros')
self.state_step = ParameterTuple(Parameter(
Tensor(0, mstype.int32), "step_"+str(i)) for i in range(len(self.parameters)))
self.increase_tensor = Tensor(1, mstype.int32)
self.op_mul = P.Mul()
self.assignadd = P.AssignAdd()
self.op_pow = P.Pow()
self.op_sqrt = P.Sqrt()
self.op_maximum = P.Maximum()
def construct(self, gradients):
for group_id, group in enumerate(self.param_groups):
params = []
grads = []
exp_avgs = []
exp_avg_sqs = []
max_exp_avg_sqs = []
state_steps = []
params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps = \
self._init_group(group, gradients, params, grads, exp_avgs, exp_avg_sqs,
max_exp_avg_sqs, state_steps, group_id)
beta1, beta2 = group['betas']
self.apply_adam(params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps,
group['amsgrad'], beta1, beta2, group['lr'], group['weight_decay'], group['eps'],
group["maximize"], group["grad_centralization"])
def apply_adam(self, params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps,
amsgrad, beta1, beta2, lr, weight_decay, eps, maximize, grad_centralization):
grads = self._decay_weight(weight_decay, params, grads)
grads = self._gradients_centralization(grad_centralization, grads)
for i, param in enumerate(params):
grad = grads[i] if not maximize else -grads[i]
exp_avg = exp_avgs[i]
exp_avg_sq = exp_avg_sqs[i]
step_t = state_steps[i]
F.assign(exp_avg, self.op_mul(exp_avg, beta1) + self.op_mul(grad, 1-beta1))
F.assign(exp_avg_sq, ops.addcmul(self.op_mul(exp_avg_sq, beta2), grad, grad.conj(), 1-beta2))
step_t = F.depend(step_t, self.assignadd(step_t, self.increase_tensor))
bias_correction1 = F.tuple_to_array((1.0,)) - self.op_pow(beta1, step_t)
bias_correction2 = F.tuple_to_array((1.0,)) - self.op_pow(beta2, step_t)
step_size = lr / bias_correction1
bias_correction2_sqrt = self.op_sqrt(bias_correction2)
if amsgrad:
F.assign(max_exp_avg_sqs[i], self.op_maximum(max_exp_avg_sqs[i], exp_avg_sq))
denom = self.op_sqrt(max_exp_avg_sqs[i]) / bias_correction2_sqrt + eps
else:
denom = self.op_sqrt(exp_avg_sq) / bias_correction2_sqrt + eps
param = F.depend(param, denom)
next_param = param - self.op_mul(exp_avg / denom, step_size)
F.assign(param, next_param)
def _init_group(self, group, gradients, params, grads, exp_avgs, exp_avg_sqs,
max_exp_avg_sqs, state_steps, group_id):
""" Initialize group params. """
p_id = self.group_start_id[group_id]
for i, param in enumerate(group["params"]):
params.append(param)
grads.append(gradients[p_id+i])
exp_avgs.append(self.exp_avg[p_id+i])
exp_avg_sqs.append(self.exp_avg_sq[p_id+i])
max_exp_avg_sqs.append(self.max_exp_avg_sq[p_id+i])
state_steps.append(self.state_step[p_id+i])
return params, grads, exp_avgs, exp_avg_sqs, max_exp_avg_sqs, state_steps