基于numpy与pandas库的定义优化器代码

下面是一个基于 NumPy 和 Pandas 库的自定义优化器代码示例：

import numpy as np
import pandas as pd

class Optimizer:
    def __init__(self, lr=0.01):
        self.lr = lr

    def update(self, params, gradients):
        pass

class SGD(Optimizer):
    def __init__(self, lr=0.01):
        super().__init__(lr)

    def update(self, params, gradients):
        for param, grad in zip(params, gradients):
            param -= self.lr * grad

class Momentum(Optimizer):
    def __init__(self, lr=0.01, momentum=0.9):
        super().__init__(lr)
        self.momentum = momentum
        self.velocities = None

    def update(self, params, gradients):
        if self.velocities is None:
            self.velocities = [np.zeros_like(param) for param in params]

        for i, (param, grad) in enumerate(zip(params, gradients)):
            self.velocities[i] = self.momentum * self.velocities[i] - self.lr * grad
            param += self.velocities[i]

class Adam(Optimizer):
    def __init__(self, lr=0.001, beta1=0.9, beta2=0.999, eps=1e-8):
        super().__init__(lr)
        self.beta1 = beta1
        self.beta2 = beta2
        self.eps = eps
        self.m = None
        self.v = None
        self.t = 0

    def update(self, params, gradients):
        if self.m is None:
            self.m = [np.zeros_like(param) for param in params]
            self.v = [np.zeros_like(param) for param in params]

        self.t += 1
        lr_t = self.lr * np.sqrt(1 - self.beta2**self.t) / (1 - self.beta1**self.t)

        for i, (param, grad) in enumerate(zip(params, gradients)):
            self.m[i] = self.beta1 * self.m[i] + (1 - self.beta1) * grad
            self.v[i] = self.beta2 * self.v[i] + (1 - self.beta2) * grad**2
            param -= lr_t * self.m[i] / (np.sqrt(self.v[i]) + self.eps)

这里定义了三种常用的优化器：随机梯度下降（SGD）、动量法（Momentum）和自适应矩估计（Adam）。每个优化器都继承自基类 `Optimizer`，并实现了 `update` 方法来更新模型参数。在更新参数时，每个优化器都使用了不同的公式来计算参数的更新量。其中，`SGD` 只使用梯度，`Momentum` 加入了动量项，而 `Adam` 则使用了动量项和自适应学习率。