admm_svm_pool.py

"""
Copyright 2013 Steven Diamond

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

# A SVM example with CVXPY.
from multiprocessing import Pool

import numpy as np

from cvxpy import Minimize, Problem, Variable, norm, pos, sum_squares

# Divide the data into NUM_PROCS segments,
# using NUM_PROCS processes.
NUM_PROCS = 4
SPLIT_SIZE = 250

# Problem data.
np.random.seed(1)
N = NUM_PROCS*SPLIT_SIZE
n = 10
offset = np.random.randn(n, 1)
data = []
for i in range(N/2):
    data += [(1, offset + np.random.normal(1.0, 2.0, (n, 1)))]
for i in range(N/2):
    data += [(-1, offset + np.random.normal(-1.0, 2.0, (n, 1)))]
data_splits = [data[i:i+SPLIT_SIZE] for i in range(0, N, SPLIT_SIZE)]

# Count misclassifications.
def get_error(w):
    error = 0
    for label, sample in data:
        if not label*(np.dot(w[:-1].T, sample) - w[-1])[0] > 0:
            error += 1
    return "%d misclassifications out of %d samples" % (error, N)

# Construct problem.
rho = 1.0
w = Variable(n + 1)

def prox(args):
    f, w_avg = args
    f += (rho/2)*sum_squares(w - w_avg)
    Problem(Minimize(f)).solve()
    return w.value

def svm(data):
    slack = [pos(1 - b*(a.T*w[:-1] - w[-1])) for (b, a) in data]
    return norm(w, 2) + sum(slack)

fi = map(svm, data_splits)
# ADMM algorithm.
pool = Pool(NUM_PROCS)
w_avg = np.zeros((n+1, 1))
u_vals = NUM_PROCS*[np.zeros((n+1, 1))]
for i in range(10):
    print(get_error(w_avg))
    prox_args = [w_avg - ui for ui in u_vals]
    w_vals = pool.map(prox, zip(fi, prox_args))
    w_avg = sum(w_vals)/len(w_vals)
    u_vals = [ui + wi - w_avg for ui, wi in zip(u_vals, w_vals)]

print(w_avg[:-1])
print(w_avg[-1])