「Deep Learning」Note on Adam

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http://blog.csdn.net/dgyuanshaofeng/article/details/80371004

基于Pytorch 0.3.0

Adam，随机优化的算法之一，在TensorFlow和Pytorch中常用，在早期深度学习里面，我们使用Caffe还是常用SGD。也有道听途说，Adam跑通网络之后，应该使用SGD再跑一次，也就是认为SGD收敛的解好于Adam的解，但是Adam可以快速验证网络是否可用。

Pytorch使用的Adam，其默认参数和论文给出的推荐参数基本一致。也就是，学习率lr为0.001，beta1为0.9，beta2为0.999，eps为1e-08。另外，默认不使用L2惩罚，也就是不使用weight decay。bete1为计算运行平均梯度的系数，而beta1为计算这个梯度的平方(square)的系数。

torch.optim.adam的源代码。

import math
import torch
from .optimizer import Optimizer

class Adam(Optimizer):
    """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)

    .. _Adam\: A Method for Stochastic Optimization:
        https://arxiv.org/abs/1412.6980
    """

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0):
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay)
        super(Adam, self).__init__(params, defaults)

    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:
            loss = closure()

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

                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.data)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p.data)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['betas']

                state['step'] += 1

                if group['weight_decay'] != 0:
                    grad = grad.add(group['weight_decay'], p.data)

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)

                denom = exp_avg_sq.sqrt().add_(group['eps'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1

                p.data.addcdiv_(-step_size, exp_avg, denom)

        return loss

源代码的说明。继承父类Optimizer。init方法为默认初始化，可见这里说明了如何使用Adam。其中，defaults将参数打包了，params为需要优化的参数列表/矩阵。

[1] Adam A Method for Stochastic Optimization 2014 [paper]