q3_sgd.py

# Save parameters every a few SGD iterations as fail-safe
SAVE_PARAMS_EVERY = 1000

import glob
import random
import numpy as np
import os.path as op
import pickle

def load_saved_params():
    """ A helper function that loads previously saved parameters and resets iteration start """
    st = 0
    for f in glob.glob("saved_params_*.npy"):
        iter = int(op.splitext(op.basename(f))[0].split("_")[2])
        if (iter > st):
            st = iter
            
    if st > 0:
        with open("saved_params_%d.npy" % st, "rb") as f:
            params = pickle.load(f)
            state = pickle.load(f)
        return st, params, state
    else:
        return st, None, None
    
def save_params(iter, params):
    with open("saved_params_%d.npy" % iter, "wb") as f:
        pickle.dump(params, f)
        pickle.dump(random.getstate(), f)

def sgd(f, x0, step, iterations, postprocessing = None, useSaved = False, PRINT_EVERY=10):
    """ Stochastic Gradient Descent """
    # Implement the stochastic gradient descent method in this        
    # function.                                                       
    
    # Inputs:                                                         
    # - f: the function to optimize, it should take a single        
    #     argument and yield two outputs, a cost and the gradient  
    #     with respect to the arguments                            
    # - x0: the initial point to start SGD from                     
    # - step: the step size for SGD                                 
    # - iterations: total iterations to run SGD for                 
    # - postprocessing: postprocessing function for the parameters  
    #     if necessary. In the case of word2vec we will need to    
    #     normalize the word vectors to have unit length.          
    # - PRINT_EVERY: specifies every how many iterations to output  

    # Output:                                                         
    # - x: the parameter value after SGD finishes  
    
    # Anneal learning rate every several iterations
    ANNEAL_EVERY = 20000
    
    if useSaved:
        start_iter, oldx, state = load_saved_params()
        if start_iter > 0:
            x0 = oldx;
            step *= 0.5 ** (start_iter / ANNEAL_EVERY)
            
        if state:
            random.setstate(state)
    else:
        start_iter = 0
    
    x = x0
    
    if not postprocessing:
        postprocessing = lambda x: x
    
    expcost = None
    
    for iter in range(start_iter + 1, iterations + 1):
        ### Don't forget to apply the postprocessing after every iteration!
        ### You might want to print the progress every few iterations.

        cost = None
        ### YOUR CODE HERE

        cost, grad = f(x)
        x -= (step / (1 + iter)) * grad
        x = postprocessing(x)
        
        ### END YOUR CODE
        
        if iter % PRINT_EVERY == 0:
            if not expcost:
                expcost = cost
            else:
                expcost = .95 * expcost + .05 * cost
            print("iter %d: %f" % (iter, expcost))
        
        if iter % SAVE_PARAMS_EVERY == 0 and useSaved:
            save_params(iter, x)
            
        if iter % ANNEAL_EVERY == 0:
            step *= 0.5
    
    return x

def sanity_check():
    quad = lambda x: (np.sum(x ** 2), x * 2)

    print("Running sanity checks...")
    t1 = sgd(quad, 0.5, 0.01, 1000, PRINT_EVERY=100)
    print("test 1 result:", t1)
    assert abs(t1) <= 1e-6

    t2 = sgd(quad, 0.0, 0.01, 1000, PRINT_EVERY=100)
    print("test 2 result:", t2)
    assert abs(t2) <= 1e-6

    t3 = sgd(quad, -1.5, 0.01, 1000, PRINT_EVERY=100)
    print("test 3 result:", t3)
    assert abs(t3) <= 1e-6
    
    print("")

def your_sanity_checks(): 
    """
    Use this space add any additional sanity checks by running:
        python q3_sgd.py 
    This function will not be called by the autograder, nor will
    your additional tests be graded.
    """
    print("Running your sanity checks...")
    ### YOUR CODE HERE
    raise NotImplementedError
    ### END YOUR CODE

if __name__ == "__main__":
    sanity_check();
    your_sanity_checks();