In [1]:

    

import random


    

In [7]:

    

def gradient_descent_update(x, gradx, learning_rate):
    """
    Performs a gradient descent update.
    """

    x = x - learning_rate * gradx
    
    return x

#import f


    

In [8]:

    

"""
Given the starting point of any `x` gradient descent
should be able to find the minimum value of x for the
cost function `f` defined below.
"""
def f(x):
    """
    Quadratic function.

    It's easy to see the minimum value of the function
    is 5 when is x=0.
    """
    return x**2 + 5


    

In [9]:

    

def df(x):
    """
    Derivative of `f` with respect to `x`.
    """
    return 2*x


    

In [19]:

    

# Random number between 0 and 10,000. Feel free to set x whatever you like.
x = random.randint(0, 10000)

# TODO: Set the learning rate
learning_rate = 0.001
epochs = 1000

for i in range(epochs+1):
    cost = f(x)
    gradx = df(x)
    if i % 25 == 0:
        print("EPOCH {}: Cost = {:.3f}, x = {:.3f}".format(i, cost, gradx))
    x = gradient_descent_update(x, gradx, learning_rate)


    

    




EPOCH 0: Cost = 72250005.000, x = 17000.000
EPOCH 25: Cost = 65367962.601, x = 16170.091
EPOCH 50: Cost = 59141456.639, x = 15380.696
EPOCH 75: Cost = 53508045.182, x = 14629.838
EPOCH 100: Cost = 48411234.093, x = 13915.636
EPOCH 125: Cost = 43799910.477, x = 13236.299
EPOCH 150: Cost = 39627830.109, x = 12590.127
EPOCH 175: Cost = 35853153.672, x = 11975.500
EPOCH 200: Cost = 32438027.176, x = 11390.877
EPOCH 225: Cost = 29348202.347, x = 10834.795
EPOCH 250: Cost = 26552693.163, x = 10305.860
EPOCH 275: Cost = 24023465.125, x = 9802.747
EPOCH 300: Cost = 21735154.106, x = 9324.194
EPOCH 325: Cost = 19664811.992, x = 8869.004
EPOCH 350: Cost = 17791676.553, x = 8436.035
EPOCH 375: Cost = 16096963.225, x = 8024.203
EPOCH 400: Cost = 14563676.733, x = 7632.476
EPOCH 425: Cost = 13176440.659, x = 7259.872
EPOCH 450: Cost = 11921343.235, x = 6905.458
EPOCH 475: Cost = 10785797.835, x = 6568.346
EPOCH 500: Cost = 9758416.747, x = 6247.691
EPOCH 525: Cost = 8828896.977, x = 5942.690
EPOCH 550: Cost = 7987916.922, x = 5652.579
EPOCH 575: Cost = 7227042.894, x = 5376.630
EPOCH 600: Cost = 6538644.538, x = 5114.153
EPOCH 625: Cost = 5915818.316, x = 4864.489
EPOCH 650: Cost = 5352318.274, x = 4627.013
EPOCH 675: Cost = 4842493.404, x = 4401.131
EPOCH 700: Cost = 4381230.974, x = 4186.276
EPOCH 725: Cost = 3963905.259, x = 3981.909
EPOCH 750: Cost = 3586331.146, x = 3787.520
EPOCH 775: Cost = 3244722.169, x = 3602.620
EPOCH 800: Cost = 2935652.534, x = 3426.746
EPOCH 825: Cost = 2656022.765, x = 3259.459
EPOCH 850: Cost = 2403028.622, x = 3100.338
EPOCH 875: Cost = 2174132.975, x = 2948.985
EPOCH 900: Cost = 1967040.368, x = 2805.021
EPOCH 925: Cost = 1779673.990, x = 2668.085
EPOCH 950: Cost = 1610154.856, x = 2537.834
EPOCH 975: Cost = 1456782.958, x = 2413.941
EPOCH 1000: Cost = 1318020.222, x = 2296.097

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