Python中的批量梯度下降算法返回了巨大的值

Question

我正在尝试在Python中实现一个批量梯度下降算法，这个算法需要输入训练数据、学习率和迭代次数，然后返回权重。但是，当我运行这个算法时，经过几次迭代后，参数的值变得非常大，最后返回了'nan'（不是一个数字）。

x = [[2104] [1600] [2400] [1416] [3000] [1985] [1534] [1427] [1380] [1494] [1940] [2000] [1890] [4478] [1268] [2300] [1320] [1236] [2609] [3031] [1767] [1888] [1604] [1962] [3890] [1100] [1458] [2526] [2200] [2637] [1839] [1000] [2040] [3137] [1811] [1437] [1239] [2132] [4215] [2162] [1664] [2238] [2567] [1200] [ 852] [1852] [1203]]

y = [399900 329900 369000 232000 539900 299900 314900 198999 212000 242500 239999 347000 329999 699900 259900 449900 299900 199900 499998 599000 252900 255000 242900 259900 573900 249900 464500 469000 475000 299900 349900 169900 314900 579900 285900 249900 229900 345000 549000 287000 368500 329900 314000 299000 179900 299900 239500]

a = 0.01

num_iter = 100

def BGD ( x, y, a, num_iter):
    m = len(x) #number of samples
    n = x.shape[1] #number of features
    p = np.zeros(n) 
    b = 0
    for _ in range(num_iter):
        sum_p = np.zeros(n)
        sum_b = 0
        for i in range(m):
            sum_p = sum_p + ((np.dot(p,x[i])+b) - y[i]) * x[i]
            sum_b = sum_b + (((np.dot(p,x[i])+b) - y[i]))
        p = p - (a * (1/m) * sum_p)   
        b = b - (a * (1/m) * sum_b)
    return p, b

p, b = BGD(x, y, 0.01, 100)
print(p)
print(b)

我得到了以下结果：

RuntimeWarning: overflow encountered in add
  sum_p = sum_p + ((np.dot(p,x[i])+b) - y[i]) * x[i]
RuntimeWarning: invalid value encountered in subtract
  p = p - (a * (1/m) * sum_p)
[nan]
nan