The following is a simple linear regression/ML code that I have modified. For all initial weight and bias (i.e. weight = np.array([0.03, 0.04, 0.02]), bias = 0.01), the training will blow up (It just won't converge).

Wonder if there is a bug in the code or how to choose good initial values (weight and bias) so it will converge.

#Adopted from http://ml-cheatsheet.readthedocs.io/en/latest/linear_regression.html
import numpy as np
from numpy import genfromtxt


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

def cost_function(X, Y, weight, bias):
    companies = X.shape[0]
    return np.sum((predict(X, weight, bias) - Y) **2) / companies



def update_weights(X, Y, weight, bias, learning_rate):
    companies = X.shape[0]

    dW = 2 * np.dot(X.T,  predict(X, weight, bias) - Y)
    db = 2 * np.sum(predict(X, weight, bias) - Y)
    """
    for i in range(companies):
        # Calculate partial derivatives
        # -2x(y - (mx + b))
        dw += -2*X[i] * (sales[i] - (weight*X[i] + bias))

        # -2(y - (mx + b))
        db += -2*(sales[i] - (weight*X[i] + bias))
    """
    #print(dW, db)
    # We subtract because the derivatives point in direction of steepest ascent
    #weight -= (dW / companies) * learning_rate
    #bias -= (db / companies) * learning_rate

    return weight - (dW / companies) * learning_rate, bias - (db / companies) * learning_rate

def train(X, Y, weight, bias, learning_rate, iters):
    cost_history = []

    for i in range(iters):
        weight,bias = update_weights(X, Y, weight, bias, learning_rate)

        #Calculate cost for auditing purposes
        cost = cost_function(X, Y, weight, bias)
        cost_history.append(cost)

        # Log Progress
        if i % 100 == 0:
            print ("iter: "+str(i) + " cost: "+str(cost) + "\n")

    return weight, bias, cost_history

#the Advertising.csv is from http://www-bcf.usc.edu/~gareth/ISL/Advertising.csv
if __name__ == "__main__":
    my_data = genfromtxt('Advertising.csv', delimiter=',')
    X = my_data[1:, 1:4:1]
    Y = my_data[1:, 4];  #the sales
    a,b, _ = train(X, Y, np.array([0.03, 0.04, 0.02]), 0.01, 0.001, 1000)

The problem is, whatever value I use as initial weight and bias (i.e. weight = np.array([0.03, 0.04, 0.02]), bias = 0.01) will cause the value to blow up. It just won't converge.
train(X, Y, weight, bias, 0.001, 1000)

UPDATE1

When I ran the above code snippet, I got

$ python linearRegression_multi.py 
iter: 0 cost: 212337.75728564826

/Users/joe/anaconda3/lib/python3.6/site-packages/numpy/core/_methods.py:32: RuntimeWarning: overflow encountered in reduce
  return umr_sum(a, axis, dtype, out, keepdims)
linearRegression_multi.py:11: RuntimeWarning: overflow encountered in square
  return np.sum((predict(X, weight, bias) - Y) **2) / companies
iter: 100 cost: inf

linearRegression_multi.py:34: RuntimeWarning: invalid value encountered in subtract
  return weight - dW * learning_rate / companies , bias - db * learning_rate / companies
iter: 200 cost: nan

iter: 300 cost: nan

iter: 400 cost: nan

iter: 500 cost: nan

iter: 600 cost: nan

iter: 700 cost: nan

iter: 800 cost: nan

iter: 900 cost: nan

solution

Figured out the cause of the problem! The learning rate in this case 0.001 is too high.

Change it to be 0.00001 works. i,e, change the last line in original snippet to be the following makes it work.

a,b, _ = train(X, Y, np.array([0.03, 0.04, 0.02]), 0.01, 0.00001, 1000)

Here is the output:

python te.py 
iter: 0 cost: 23.07411798374272

iter: 100 cost: 6.479930413738248

iter: 200 cost: 5.097751463999494

iter: 300 cost: 4.528064099014893

iter: 400 cost: 4.263917598438141

iter: 500 cost: 4.1398851132621655

iter: 600 cost: 4.081383875535448

iter: 700 cost: 4.053584811192947

iter: 800 cost: 4.040172367398533

iter: 900 cost: 4.033501506011401