pytorch.optimizer 优化算法

Posted 2022-02-02 东东就是我

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https://zhuanlan.zhihu.com/p/346205754
https://blog.csdn.net/google19890102/article/details/69942970
https://zhuanlan.zhihu.com/p/32626442
https://zhuanlan.zhihu.com/p/32230623

1.优化器optimizer

import torch
import numpy as np
import warnings
warnings.filterwarnings('ignore') #ignore warnings

x = torch.linspace(-np.pi, np.pi, 2000)
y = torch.sin(x)

p = torch.tensor([1, 2, 3])
xx = x.unsqueeze(-1).pow(p)

model = torch.nn.Sequential(
    torch.nn.Linear(3, 1),
    torch.nn.Flatten(0, 1)
)
loss_fn = torch.nn.MSELoss(reduction='sum')

learning_rate = 1e-3
optimizer = torch.optim.RMSprop(model.parameters(), lr=learning_rate)
for t in range(1, 1001):
    y_pred = model(xx)
    loss = loss_fn(y_pred, y)
    if t % 100 == 0:
        print('No.: 5d, loss: :.6f'.format(t, loss.item()))
    optimizer.zero_grad() # 梯度清零
    loss.backward() # 反向传播计算梯度
    optimizer.step() # 梯度下降法更新参数

1.1step才是更新参数

    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:
            weight_decay = group['weight_decay']
            momentum = group['momentum']
            dampening = group['dampening']
            nesterov = group['nesterov']

            for p in group['params']:
                if p.grad is None:
                    continue
                d_p = p.grad  #获取参数梯度
                if weight_decay != 0:
                    d_p = d_p.add(p, alpha=weight_decay) 
                if momentum != 0:
                    param_state = self.state[p]
                    if 'momentum_buffer' not in param_state:
                        buf = param_state['momentum_buffer'] = torch.clone(d_p).detach()
                    else:
                        buf = param_state['momentum_buffer']
                        buf.mul_(momentum).add_(d_p, alpha=1 - dampening)
                    if nesterov:
                        d_p = d_p.add(buf, alpha=momentum)
                    else:
                        d_p = buf

                p.add_(d_p, alpha=-group['lr']) #更新参数

        return loss

1.0 常见优化器变量定义

模型参数
$\\theta$ ,
目标函数
$J(\\theta)$
每一个时刻t（假设是一个batch）的梯度
$g_t=\\bigtriangledown _\\thetaJ(\\theta)$
学习率为
$\\eta$
根据历史梯度的一阶动量
$m_t=\\phi (g_1,g_2,...g_t)$
根据历史梯度的二阶动量
$v_t=\\psi (g_1,g_2,...g_t)$
更新模型参数
$\\theta_t+1=\\theta_t-\\frac1\\sqrtv_t+\\epsilon m_t$ ,
平滑项，防止分母为0