用代码自己实现Adam算法

Adam (Adaptive Moment Estimation) 是一种常用的优化算法，它结合了梯度下降法（SGD）的优点以及动量法（Momentum）的稳定性能。以下是使用 Python 和 PyTorch 实现 Adam 算法的基本步骤：

import torch
from torch.optim import Optimizer

class CustomAdam(Optimizer):
    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(CustomAdam, self).__init__(params, defaults)

    def step(self, closure=None):
        """Performs a single optimization step."""
        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  # 获取梯度
                state = self.state[p]

                # 如果这是第一个迭代，则初始化 m 和 v（移动平均和指数移动平均）
                if 'momentum_buffer' not in state:
                    state['momentum_buffer'] = torch.zeros_like(p.data)
                    state['step'] = 0
                    state['exp_avg'] = torch.zeros_like(p.data)
                    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  # 更新步数

                # 计算 bias-corrected first and second moments
                if group['weight_decay'] != 0:
                    exp_avg.mul_(beta1).add_(grad, alpha=1 - beta1)
                    exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1 - beta2)
                else:
                    exp_avg.mul_(beta1).add_(grad)
                    exp_avg_sq.mul_(beta2).addcmul_(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)  # 更新参数

        return loss

# 使用示例
model.parameters(), lr=0.001)

这个自定义的 Adam 类实现了基本的 Adam 更新规则。注意，为了保持兼容性，你需要导入 `math` 模块，并且将 `state['exp_avg']` 和 `state['exp_avg_sq']` 替换为你所需的移动平均变量名。