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 cPickle as 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, "r") 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, "w") 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 """

    # 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.    
    # - 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 xrange(start_iter + 1, iterations + 1):

        cost = None
        cost, gradx = f(x)
        x += - step*gradx
        
        x = postprocessing(x)
        
        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 ""

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