Python中常见优化器（Optimizer）算法性能对比

在Python中，常见的优化器算法有梯度下降（Gradient Descent）、随机梯度下降（Stochastic Gradient Descent）、动量优化器（Momentum Optimizer）、Adam优化器（Adam Optimizer）等。本文将使用一个简单的线性回归模型来比较这些优化器算法的性能。

首先，我们导入必要的库和数据集：

import numpy as np
from sklearn.datasets import make_regression
from sklearn.model_selection import train_test_split

# 生成线性回归数据集
X, y = make_regression(n_samples=1000, n_features=10, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

接下来，我们定义一个简单的线性回归模型：

class LinearRegression:
    def __init__(self, lr=0.001):
        self.lr = lr
        self.weights = None
        self.bias = None

    def fit(self, X, y, epochs=100):
        n_samples, n_features = X.shape
        self.weights = np.zeros(n_features)
        self.bias = 0
        
        for _ in range(epochs):
            y_pred = self.predict(X)
            dw = (1/n_samples) * np.dot(X.T, (y_pred - y))
            db = (1/n_samples) * np.sum(y_pred - y)
            self.weights -= self.lr * dw
            self.bias -= self.lr * db

    def predict(self, X):
        return np.dot(X, self.weights) + self.bias

接下来，我们使用上述定义的线性回归模型，并比较不同优化器算法的性能：

from sklearn.metrics import mean_squared_error

lr = 0.001
epochs = 100

optimizers = ['Gradient Descent', 'Stochastic Gradient Descent', 'Momentum Optimizer', 'Adam Optimizer']
mse_results = []

# 梯度下降
model = LinearRegression(lr=lr)
model.fit(X_train, y_train, epochs=epochs)
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
mse_results.append(mse)

# 随机梯度下降
model = LinearRegression(lr=lr)
for _ in range(epochs):
    for i in range(len(X_train)):
        idx = np.random.randint(len(X_train))
        xi, yi = X_train[idx], y_train[idx]
        model.fit(xi.reshape(1, -1), yi.reshape(1, -1))
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
mse_results.append(mse)

# 动量优化器
model = LinearRegression(lr=lr)
gamma = 0.9
v = np.zeros(X_train.shape[1])
for _ in range(epochs):
    for i in range(len(X_train)):
        xi, yi = X_train[i], y_train[i]
        y_pred = model.predict(xi.reshape(1, -1))
        dw = (1/len(X_train)) * np.dot(xi.T, (y_pred - yi))
        db = (1/len(X_train)) * np.sum(y_pred - yi)
        v = gamma * v + lr * dw
        model.weights -= v
        model.bias -= lr * db
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
mse_results.append(mse)

# Adam优化器
model = LinearRegression(lr=lr)
beta1 = 0.9
beta2 = 0.999
epsilon = 1e-8
m = np.zeros(X_train.shape[1])
v = np.zeros(X_train.shape[1])
for _ in range(epochs):
    for i in range(len(X_train)):
        xi, yi = X_train[i], y_train[i]
        y_pred = model.predict(xi.reshape(1, -1))
        dw = (1/len(X_train)) * np.dot(xi.T, (y_pred - yi))
        db = (1/len(X_train)) * np.sum(y_pred - yi)
        m = beta1 * m + (1 - beta1) * dw
        v = beta2 * v + (1 - beta2) * (dw ** 2)
        m_hat = m / (1 - beta1)
        v_hat = v / (1 - beta2)
        model.weights -= lr * m_hat / (np.sqrt(v_hat) + epsilon)
        model.bias -= lr * db
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
mse_results.append(mse)

# 打印结果
for optimizer, mse in zip(optimizers, mse_results):
    print(f"{optimizer}: Mean Squared Error = {mse}")

以上代码中，我们分别使用不同的优化器算法来训练线性回归模型，并计算其在测试集上的均方误差（Mean Squared Error）。最后，我们将不同优化器算法的性能进行比较。

通过运行上述代码，我们可以得到不同优化器算法的性能对比结果。记住，每次运行结果可能会有所不同，因为我们使用随机梯度下降和Adam优化器时，每次迭代都使用了不同的训练样本。

这里的例子只是一个简单的线性回归模型，实际上，在复杂的神经网络模型中，不同的优化器算法可能会有不同的表现。因此，选择合适的优化器算法对于训练模型的性能和收敛速度非常重要。