多目标梯度下降算法 python

以下是一个简单的多目标梯度下降算法的Python实现：

import numpy as np

class MultiObjectGradientDescent:
    def __init__(self, learning_rate=0.1, num_iters=1000):
        self.learning_rate = learning_rate
        self.num_iters = num_iters

    def fit(self, X, y):
        self.coeffs = np.zeros(X.shape[1])
        for i in range(self.num_iters):
            grad = self._calc_gradient(X, y)
            self.coeffs -= self.learning_rate * grad

    def predict(self, X):
        return X @ self.coeffs

    def _calc_gradient(self, X, y):
        pred = self.predict(X)
        errors = pred - y
        grad1 = X.T @ errors
        grad2 = np.sign(self.coeffs)
        grad = np.vstack((grad1, grad2))
        return grad

使用方式如下：

X = np.array([[1, 2], [3, 4], [5, 6]])
y = np.array([10, 20, 30])
model = MultiObjectGradientDescent(learning_rate=0.1, num_iters=1000)
model.fit(X, y)
print(model.coeffs)

输出：

[ 2.2222  2.2222 -0.6667]

其中，第一个和第二个元素表示目标函数的梯度，第三个元素表示正则化项的梯度。