梯度下降法在功能拟合中的问题

Question

我试图使用假设类csigmoid（ax + b）来使用梯度下降的方法将x <0的图g（x）= 1和x> 0的g（x）= 2x + 1匹配+ d，其中a，b，c，d是参数。我选择的损失函数是平方损失误差。但是，我从以下代码中得到的结果显然是不正确的。

import math

cur_a = 1
cur_b = 3
cur_c = 3
cur_d = 3
rate = 0.0000000000001

def sigmoid(x):
    return 1 / (1 + math.exp(-x))

data = [[-1, 1.0], [-0.75, 1.0], [-0.5, 1.0], [-0.25, 1], [0, 1], [0.25, 1.5], [0.5, 2], [0.75, 2.5], [1, 3], [1.25, 3.5], [1.5, 4]]

def gradienta():
    result = 0
    for i in range(len(data)):
        ele = data[i]
        result += 2 * (cur_c * sigmoid(cur_a * ele[0] + cur_b) + cur_d - ele[1]) * cur_c * sigmoid(
            cur_a * ele[0] + cur_b) * (1 - sigmoid(cur_a * ele[0] + cur_b)) * ele[0]
    return result/len(data)


def gradientb():
    result = 0
    for i in range(len(data)):
        ele = data[i]
        result += 2 * (cur_c * sigmoid(cur_a * ele[0] + cur_b) + cur_d - ele[1]) * cur_c * sigmoid(
            cur_a * ele[0] + cur_b) * (1 - sigmoid(cur_a * ele[0] + cur_b))
    return result/len(data)


def gradientc():
    result = 0
    for i in range(len(data)):
        ele = data[i]
        result += 2 * (cur_c * sigmoid(cur_a * ele[0] + cur_b) + cur_d - ele[1]) * sigmoid(
           cur_a * ele[0] + cur_b)
    return result/len(data)


def gradientd():
    result = 0;
    for i in range(len(data)):
        ele = data[i]
        result += 2 * cur_c * sigmoid(cur_a * ele[0] + cur_b) + cur_d - ele[1]
    return result/len(data)

iters = 0
max_iters = 10000
precision = 0.00001
step_size = 1

while step_size > precision and iters < max_iters:
    # save previous location
    prev_a = cur_a
    prev_b = cur_b
    prev_c = cur_c
    prev_d = cur_d

    # move to new location according to steepest descent
    cur_a = cur_a - rate * gradienta()
    cur_b = cur_a - rate * gradientb()
    cur_c = cur_a - rate * gradientc()
    cur_d = cur_a - rate * gradientd()

    # update step_size and iters
    step_size = ((prev_a - cur_a) ** 2 + (prev_b - cur_b) ** 2 + (prev_c - cur_c) ** 2 + (prev_d - cur_d) ** 2) ** 0.5
    iters += 1

print(cur_a)
print(cur_b)
print(cur_c)
print(cur_d)

虽然d的值似乎合理，但我希望a，b和c的值在5和10左右。但是，代码的输出是

1.0000000000000535

1.0000000000000615

1.0000000000003113

1.0000000000001017

其中每个值对应一个参数。这不是一个很好的匹配。

关于哪里出了问题的任何建议？