pytorch api:torch.optim.Adam

torch.optim.Adam(params, lr=0.001, betas=(0.9, 0.999), eps=1e-08, weight_decay=0, amsgrad=False)

Implements Adam algorithm.

It has been proposed in Adam: A Method for Stochastic Optimization.

Parameters

• params (iterable) – iterable of parameters to optimize or dicts defining parameter groups

• lr (float, optional) – learning rate (default: 1e-3)

• betas (Tuple[float,float], optional) – coefficients used for computing running averages of gradient and its square (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 (boolean, optional) – whether to use the AMSGrad variant of this algorithm from the paper On the Convergence of Adam and Beyond (default: False)

step(closure=None)

Performs a single optimization step.

Parameters

closure (callable, optional) – A closure that reevaluates the model and returns the loss.

SOURCE CODE

import math
import torch
from .optimizer import Optimizer

[[docs]](https://pytorch.org/docs/master/optim.html#torch.optim.Adam)class Adam(Optimizer):
    r"""Implements Adam algorithm.

 It has been proposed in `Adam: A Method for Stochastic Optimization`_.

 Arguments:
 params (iterable): iterable of parameters to optimize or dicts defining
 parameter groups
 lr (float, optional): learning rate (default: 1e-3)
 betas (Tuple[float, float], optional): coefficients used for computing
 running averages of gradient and its square (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 (boolean, optional): whether to use the AMSGrad variant of this
 algorithm from the paper `On the Convergence of Adam and Beyond`_
 (default: False)

 .. _Adam\: A Method for Stochastic Optimization:
 https://arxiv.org/abs/1412.6980
 .. _On the Convergence of Adam and Beyond:
 https://openreview.net/forum?id=ryQu7f-RZ
 """

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, amsgrad=False):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 <= eps:
            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 not 0.0 <= weight_decay:
            raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, amsgrad=amsgrad)
        super(Adam, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(Adam, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault('amsgrad', False)

[[docs]](https://pytorch.org/docs/master/optim.html#torch.optim.Adam.step)    @torch.no_grad()
    def step(self, closure=None):
        """Performs a single optimization step.

 Arguments:
 closure (callable, optional): A closure that reevaluates the model
 and returns the loss.
 """
        loss = None
        if closure is not None:
            with torch.enable_grad():
                loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad
                if grad.is_sparse:
                    raise RuntimeError('Adam does not support sparse gradients, please consider SparseAdam instead')
                amsgrad = group['amsgrad']

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
                    if amsgrad:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state['max_exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                if amsgrad:
                    max_exp_avg_sq = state['max_exp_avg_sq']
                beta1, beta2 = group['betas']

                state['step'] += 1
                bias_correction1 = 1 - beta1 ** state['step']  # equation 1
                bias_correction2 = 1 - beta2 ** state['step']  # equation 2

                if group['weight_decay'] != 0:
                    grad = grad.add(p, alpha=group['weight_decay'])  # equation 3

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)  # equation 4
                exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)  # equation 5
                if amsgrad:
                    # Maintains the maximum of all 2nd moment running avg. till now
                    torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)  # equation 6
                    # Use the max. for normalizing running avg. of gradient
                    denom = (max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])  # equation 7
                else:
                    denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])  # equation 7

                step_size = group['lr'] / bias_correction1  # equation 8

                p.addcdiv_(exp_avg, denom, value=-step_size)  # equation 9

        return loss

Equation

• equation 1 :
• equation 2 :
• equation 3 :
• equation 4 :
• equation 5 :
• equation 6 :
• equation 7 :
• equation 8 :
• equation 9 :

参考链接:
https://pytorch.org/docs/master/_modules/torch/optim/adam.html#Adam