-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathsolver_dcd_python.py
241 lines (173 loc) · 7.46 KB
/
solver_dcd_python.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
#!/usr/bin/env python2.6
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# Written (W) 2011-2012 Christian Widmer
# Copyright (C) 2011-2012 Max-Planck-Society
"""
Created on 09.12.2011
@author: Christian Widmer
@summary: Prototype of dual coordinate descend solver in python
This module provides implementation of our MTL DCD solver
with and without LibLinear's shrinking strategy.
"""
import random
import numpy as np
from base import compute_primal_objective, compute_dual_objective, alphas_to_w, v_to_w, BaseSolver
class DcdSolver(BaseSolver):
"""
solver using dual coordinate descend solver prototype
"""
def solve(self, C, all_xt, all_lt, task_indicator, M, L, record_progress=False):
"""
impementation of our dual coordinate descend solver
"""
num_xt = len(all_xt)
num_tasks = M.shape[0]
num_dim = len(all_xt[0])
V = np.zeros((num_tasks, num_dim))
alphas = np.zeros(num_xt)
# we stop here
optimal = False
primal_obj = []
dual_obj = []
#while not optimal:
for iteration in xrange(500):
# dual coordinate descend: touch one example at a time
for i in xrange(num_xt):
# current task id
ti = task_indicator[i]
# the heart of the beast: the update
inner_sum = 0
for t in xrange(num_tasks):
inner_sum += M[t,ti] * all_lt[i] * np.dot(V[t,:], all_xt[i])
d = (1.0 - inner_sum) / np.dot(all_xt[i], all_xt[i])
# store previous alpha
alpha_old = alphas[i]
# project onto feasible set
alphas[i] = max(0, min(C, alphas[i] + d))
# update w for example
V[ti,:] += (alphas[i] - alpha_old) * all_lt[i] * all_xt[i]
# keep track of objectives
if record_progress and iteration < 3 and i % 5 == 0 :
# compute objective after outer iteration
W_tmp = alphas_to_w(alphas, all_xt, all_lt, task_indicator, M).reshape(num_tasks * num_dim)
primal_obj.append(compute_primal_objective(W_tmp, C, all_xt, all_lt, task_indicator, L))
dual_obj.append(compute_dual_objective(alphas, all_xt, all_lt, task_indicator, M))
# compute W from alphas
W = alphas_to_w(alphas, all_xt, all_lt, task_indicator, M)
W2 = v_to_w(V, all_xt, all_lt, task_indicator, M)
# record final obj
self.dual_obj = compute_dual_objective(alphas, all_xt, all_lt, task_indicator, M)
self.primal_obj = compute_primal_objective(W.reshape(num_tasks * num_dim), C, all_xt, all_lt, task_indicator, L)
return True
class DcdSolverShrinking(BaseSolver):
"""
solver using dual coordinate descend solver prototype
"""
def solve(self, C, all_xt, all_lt, task_indicator, M, L, record_progress=False):
"""
impementation of our dual coordinate descend solver
including lib linears shrinking strategy
"""
num_xt = len(all_xt)
num_tasks = M.shape[0]
num_dim = len(all_xt[0])
V = np.zeros((num_tasks, num_dim))
alphas = np.zeros(num_xt)
# we stop here
optimal = False
primal_obj = []
dual_obj = []
# indices of active set
active_idx = range(num_xt)
remove_list = []
# set up projected gradients
PG = None
PGmax_old = float("inf")
PGmin_old = float("-inf")
PGmax_new = None
PGmin_new = None
epsilon = 0.00001
#while not optimal:
#TODO use other criterion
for iteration in xrange(500):
#print "removing:", len(remove_list), "remaining:", len(active_idx)
# shrink active set
active_idx = list(set(active_idx) - set(remove_list))
remove_list = []
# process in random order
random.shuffle(active_idx)
PGmax_new = float("-inf")
PGmin_new = float("inf")
#print "iteration", iteration
# dual coordinate descend: touch one example at a time
for i in active_idx:
# current task id
ti = task_indicator[i]
# the heart of the beast: the update
inner_sum = 0
for t in xrange(num_tasks):
inner_sum += M[t,ti] * all_lt[i] * np.dot(V[t,:], all_xt[i])
# this term corresponds to G in LibLinear
G = inner_sum - 1.0
################
# take care of shrinking
PG = 0
if alphas[i] == 0:
if G > PGmax_old:
remove_list.append(i)
continue
elif G < 0:
PG = G
elif alphas[i] == C:
if G < PGmin_old:
remove_list.append(i)
continue
elif G > 0:
PG = G
else:
PG = G
PGmax_new = max(PGmax_new, PG)
PGmin_new = min(PGmin_new, PG)
################
# update distance
d = -G / np.dot(all_xt[i], all_xt[i])
# store previous alpha
alpha_old = alphas[i]
# project onto feasible set
alphas[i] = max(0, min(C, alphas[i] + d))
# update w for example
V[ti,:] += (alphas[i] - alpha_old) * all_lt[i] * all_xt[i]
# update projected gradients
PGmax_old = PGmax_new
PGmin_old = PGmin_new
if PGmax_old <= 0:
PGmax_old = float("inf")
if PGmin_old >= 0:
PGmin_old = float("-inf")
# keep track of objectives
#if iteration < 3 and i % 5 == 0 :
if False:
# compute objective after outer iteration
W_tmp = alphas_to_w(alphas, all_xt, all_lt, task_indicator, M).reshape(num_tasks * num_dim)
#W_tmp = W.reshape(num_tasks * num_dim)
primal_obj.append(compute_primal_objective(W_tmp, C, all_xt, all_lt, task_indicator, L))
dual_obj.append(compute_dual_objective(alphas, all_xt, all_lt, task_indicator, M))
# check stop criterion
# compute gap
gap = PGmax_new - PGmin_new
# print gap
if gap <= epsilon:
print "terminating after iteration", iteration, " with active set size", len(active_idx)
break
# compute W from alphas
self.W = alphas_to_w(alphas, all_xt, all_lt, task_indicator, M)
W2 = v_to_w(V, all_xt, all_lt, task_indicator, M)
self.alphas = alphas
# record final obj
self.dual_obj = compute_dual_objective(alphas, all_xt, all_lt, task_indicator, M)
self.primal_obj = compute_primal_objective(self.W.reshape(num_tasks * num_dim), C, all_xt, all_lt, task_indicator, L)
return True