Hello everybody!
How are you? 
I have a doubt related to the gradient descent algorithm used in the last lab of the week.
If I understood the algorithm correctly, one of the exit conditions is that the derivatives of w and b are 0 (that is, that both parameters do not change anymore), but I cannot see that condition reflected in the code. From what I understand, the code finishes executing after a certain number of loops. What would be my mistake?
def gradient_descent(x, y, w_in, b_in, alpha, num_iters, cost_function, gradient_function):
"""
Performs gradient descent to fit w,b. Updates w,b by taking
num_iters gradient steps with learning rate alpha
Args:
x (ndarray (m,)) : Data, m examples
y (ndarray (m,)) : target values
w_in,b_in (scalar): initial values of model parameters
alpha (float): Learning rate
num_iters (int): number of iterations to run gradient descent
cost_function: function to call to produce cost
gradient_function: function to call to produce gradient
Returns:
w (scalar): Updated value of parameter after running gradient descent
b (scalar): Updated value of parameter after running gradient descent
J_history (List): History of cost values
p_history (list): History of parameters [w,b]
"""
w = copy.deepcopy(w_in) # avoid modifying global w_in
# An array to store cost J and w's at each iteration primarily for graphing later
J_history = []
p_history = []
b = b_in
w = w_in
for i in range(num_iters):
# Calculate the gradient and update the parameters using gradient_function
dj_dw, dj_db = gradient_function(x, y, w , b)
# Update Parameters using equation (3) above
b = b - alpha * dj_db
w = w - alpha * dj_dw
# Save cost J at each iteration
if i<100000: # prevent resource exhaustion
J_history.append( cost_function(x, y, w , b))
p_history.append([w,b])
# Print cost every at intervals 10 times or as many iterations if < 10
if i% math.ceil(num_iters/10) == 0:
print(f"Iteration {i:4}: Cost {J_history[-1]:0.2e} ",
f"dj_dw: {dj_dw: 0.3e}, dj_db: {dj_db: 0.3e} ",
f"w: {w: 0.3e}, b:{b: 0.5e}")
return w, b, J_history, p_history #return w and J,w history for graphing
Thank you very much in advance for your time and I apologize for the inconvenience caused!
so I am back at it with trying to instead find a meaningful definition for convergence.
.