cvx和梯度下降求解逻辑回归问题时参数结果不一致，如何解决？

Question

如题，我在用CVX和GD两种方法来求解一个逻辑回归问题，问题如下
在常规逻辑回归的基础上添加了L2正则项来约束w,b

我的代码如下

import numpy as np
import cvxpy as cp
N = 50
mi = 5
# 数据点一共N * mi个，用的是集中训练
C = 1
alpha = 0.001
eps = 1e-8
def logistic_loss(w, b, x, y):
    z = np.dot(x, w) + b
    return np.log(1 + np.exp(-y * z))

def gradient_logistic_loss(w, b, x, y):
    z = np.dot(x, w) + b
    common_term = -y / (1 + np.exp(y * z))
    grad_w = common_term * x
    grad_b = common_term
    return grad_w, grad_b

def optimal_solution_overall_GD(pc, labels):
    d = pc[0][0].shape[0]
    w_opt = np.zeros(d)
    b_opt = 0
    g_w = np.zeros(d)
    g_b = 0
    iteration = 0
    while True:
        sum_w = np.zeros(d)
        sum_b = 0
        iteration += 1
        for i in range(N):
            for j in range(mi):
                grad_w, grad_b = gradient_logistic_loss(w_opt, b_opt, pc[i][j], labels[i][j])
                sum_w += grad_w#累加梯度
                sum_b += grad_b
        g_w = sum_w / (N * mi) + C * w_opt
        g_b = sum_b / (N * mi) + C * b_opt
        w_opt -= alpha * g_w
        b_opt -= alpha * g_b
        if(iteration % 2000 == 0):
            print("iteration_GD", format(iteration))
            print("g_w", format(g_w))
            print("g_b", format(g_b))
            print(w_opt)
            print(b_opt)

        if np.all(np.abs(g_w) < eps) and np.all(np.abs(g_b) < eps):
            break
    return w_opt, b_opt

def logistic_loss_cvx(w, b, x, y):
    z = x @ w + b
    return cp.logistic(-y * z)
def optimal_solution_cvx(pc, labels, C):
    d = pc[0][0].shape[0]
    w = cp.Variable(d)
    b = cp.Variable()
    total_loss = 0
    for i in range(N):
        for j in range(mi):
            total_loss += logistic_loss_cvx(w, b, pc[i][j], labels[i][j])
    # 添加L2正则项
    total_loss += C/2 * (cp.norm(w, 2) + cp.norm(b, 2))
    # 定义优化问题
    problem = cp.Problem(cp.Minimize(total_loss))
    # 求解优化问题
    problem.solve()
    return w.value, b.value

def loss_caculate(w, b, pc, labels):
    loss = 0
    for i in range(N):
        for j in range(mi):
            loss += np.log(1 + np.exp(-labels[i][j] * (np.dot(w, pc[i][j]) + b)))
    loss = loss + C/2 * (np.linalg.norm(w, 2) + b**2)
    return loss
def main():
    # 数据集pc和标签labels都是随机的
    pc = np.random.rand(N, mi, 2)*100
    labels = np.random.choice([1, -1], size=(N, mi))
    w_GD, b_GD = optimal_solution_overall_GD(pc, labels)
    w_cvx, b_cvx = optimal_solution_cvx(pc, labels, C)
    loss1 = loss_caculate(w_GD, b_GD, pc, labels)
    loss2 = loss_caculate(w_cvx, b_cvx, pc, labels)
    print("w_GD", w_GD)
    print("w_cvx", w_cvx)
    print("b_GD", b_GD)
    print("b_cvx", b_cvx)
    print("loss1", loss1)
    print("loss2", loss2)
if __name__ == "__main__":
    main()

部分的输出如下：（因为数据随机，所以结果不固定）|

w_GD [ 0.00223391 -0.00296834]
w_cvx [ 0.00309932 -0.00200936]
b_GD -0.005593343606514088
b_cvx -0.11333700307375219
loss1 172.80617003109705
loss2 172.7096589915864

可以看出wb的值，两种方法得出的结果并不同
目前不知道是哪一个方法出了问题
问题目标是让两个结果达成近似的一致

Answer 1

参考答案有吗？