-
Notifications
You must be signed in to change notification settings - Fork 33
/
test_optimizer.py
1061 lines (928 loc) · 42.8 KB
/
test_optimizer.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
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements. See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership. The ASF licenses this file
# to you 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.
import numpy as np
import mxnet as mx
import mxnet.lr_scheduler as lr_scheduler
from mxnet import gluon
import unittest
from nose.tools import raises
import math
from mxnet.test_utils import *
from common import setup_module, with_seed, teardown
@with_seed()
def test_learning_rate():
o1 = mx.optimizer.Optimizer(learning_rate=0.01)
o1.set_learning_rate(0.2)
assert o1.learning_rate == 0.2
lr_s = lr_scheduler.FactorScheduler(step=1)
o2 = mx.optimizer.Optimizer(lr_scheduler=lr_s, learning_rate=0.3)
assert o2.learning_rate == 0.3
o2.lr_scheduler.base_lr = 0.4
assert o2.learning_rate == 0.4
@raises(UserWarning)
@with_seed()
def test_learning_rate_expect_user_warning():
lr_s = lr_scheduler.FactorScheduler(step=1)
o = mx.optimizer.Optimizer(lr_scheduler=lr_s, learning_rate=0.3)
o.set_learning_rate(0.5)
@with_seed()
def test_lr_wd_mult():
data = mx.sym.Variable('data')
bias = mx.sym.Variable('fc1_bias', lr_mult=1.0)
fc1 = mx.sym.FullyConnected(data=data, bias=bias, name='fc1', num_hidden=10, lr_mult=0)
fc2 = mx.sym.FullyConnected(data=fc1, name='fc2', num_hidden=10, wd_mult=0.5)
mod = mx.mod.Module(symbol=fc2, label_names=None, context=default_context())
mod.bind(data_shapes=[('data', (5,10))])
mod.init_params(initializer=mx.init.Uniform(1.0))
mod.init_optimizer(optimizer_params={'learning_rate': 1.0})
args1, _ = mod.get_params()
args1 = {k: v.asnumpy() for k, v in args1.items()}
mod.forward(mx.io.DataBatch(data=[mx.random.uniform(low=-1.0, high=1.0, shape=(5,10))], label=None), is_train=True)
mod.backward(mod.get_outputs())
mod.update()
args2, _ = mod.get_params()
args2 = {k: v.asnumpy() for k, v in args2.items()}
assert mod._optimizer.lr_mult == {'fc1_bias': 1.0, 'fc1_weight': 0.0}
assert mod._optimizer.wd_mult == {'fc2_bias': 0.5, 'fc2_weight': 0.5, 'fc1_bias': 0.0}
assert mx.test_utils.almost_equal(args1['fc1_weight'], args2['fc1_weight'], 1e-10)
assert not mx.test_utils.almost_equal(args1['fc1_bias'], args2['fc1_bias'], 1e-1)
assert not mx.test_utils.almost_equal(args1['fc2_weight'], args2['fc2_weight'], 1e-1)
# SGD
class PySGD(mx.optimizer.Optimizer):
"""python reference implemenation of sgd"""
def __init__(self, learning_rate=0.01, momentum=0.0, multi_precision=False, **kwargs):
super(PySGD, self).__init__(learning_rate=learning_rate, **kwargs)
self.momentum = momentum
self.multi_precision = multi_precision
def create_state(self, index, weight):
"""Create additional optimizer state: momentum
Parameters
----------
weight : NDArray
The weight data
"""
momentum = None
weight_master_copy = None
do_multi_precision = self.multi_precision and weight.dtype == np.float16
if do_multi_precision:
if self.momentum != 0.0:
momentum = mx.nd.zeros(weight.shape, weight.context, dtype=np.float32)
weight_master_copy = array(weight, ctx=weight.context, dtype=np.float32)
return (momentum, weight_master_copy)
else:
if self.momentum != 0.0:
momentum = mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)
return momentum
def create_state_multi_precision(self, index, weight):
return self.create_state(index, weight)
def update(self, index, weight, grad, state):
"""Update the parameters.
Parameters
----------
index : int
An unique integer key used to index the parameters
weight : NDArray
weight ndarray
grad : NDArray
grad ndarray
state : NDArray or other objects returned by init_state
The auxiliary state used in optimization.
"""
lr = self._get_lr(index)
wd = self._get_wd(index)
self._update_count(index)
use_multi_precision = isinstance(state, list) or isinstance(state, tuple)
if not use_multi_precision:
if self.momentum == 0.0:
if self.clip_gradient is not None:
weight[:] = ((1 - lr*wd)*weight -
lr*mx.nd.clip(grad*self.rescale_grad, -self.clip_gradient, self.clip_gradient))
else:
weight[:] = (1 - lr*wd)*weight - lr*self.rescale_grad*grad
else:
mom = state
if self.clip_gradient is not None:
mom[:] = (self.momentum*mom - lr*wd*weight -
lr*mx.nd.clip(grad*self.rescale_grad, -self.clip_gradient, self.clip_gradient))
weight += mom
else:
mom[:] = self.momentum*mom - lr*wd*weight - lr*self.rescale_grad*grad
weight += mom
else:
grad32 = array(grad, ctx=grad.context, dtype=np.float32)
mom = state[0]
weight32 = state[1]
if self.momentum == 0.0:
if self.clip_gradient is not None:
weight32[:] = ((1 - lr*wd)*weight32 -
lr*mx.nd.clip(grad32*self.rescale_grad, -self.clip_gradient, self.clip_gradient))
else:
weight32[:] = (1 - lr*wd)*weight32 - lr*self.rescale_grad*grad32
else:
if self.clip_gradient is not None:
mom[:] = (self.momentum*mom - lr*wd*weight32 -
lr*mx.nd.clip(grad32*self.rescale_grad, -self.clip_gradient, self.clip_gradient))
weight32 += mom
else:
mom[:] = self.momentum*mom - lr*wd*weight32 - lr*self.rescale_grad*grad32
weight32 += mom
tmp = weight32.astype(weight.dtype)
tmp.copyto(weight)
def update_multi_precision(self, index, weight, grad, state):
self.update(index, weight, grad, state)
@with_seed()
def test_sgd():
opt1 = PySGD
opt2 = mx.optimizer.SGD
shape = (3, 4, 5)
mom_options = [{}, {'momentum': 0.9}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
mp_options = [{}, {'multi_precision': False}, {'multi_precision': True}]
for dtype in [np.float16, np.float32, np.float64]:
for mom_option in mom_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in mp_options:
kwarg = {}
kwarg.update(mom_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
if (dtype == np.float16 and
('multi_precision' not in kwarg or
not kwarg['multi_precision'])):
continue
if dtype == np.float16:
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype, rtol=1e-3)
else:
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype)
# test operator fallback on cpu
if dtype != np.float16:
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape[:2],
dtype, w_stype='csr', g_stype='csr')
class PySparseSGD(mx.optimizer.Optimizer):
"""python reference implemenation of sgd"""
def __init__(self, learning_rate=0.01, momentum=0.0, **kwargs):
super(PySparseSGD, self).__init__(learning_rate=learning_rate, **kwargs)
self.momentum = momentum
def create_state(self, index, weight):
"""Create additional optimizer state: momentum
Parameters
----------
weight : NDArray
The weight data
"""
if self.momentum == 0.0:
return None
else:
return mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)
def update(self, index, weight, grad, state):
"""Update the parameters.
Parameters
----------
index : int
An unique integer key used to index the parameters
weight : NDArray
weight ndarray
grad : NDArray
grad ndarray
state : NDArray or other objects returned by init_state
The auxiliary state used in optimization.
"""
lr = self._get_lr(index)
wd = self._get_wd(index)
self._update_count(index)
num_rows = weight.shape[0]
if self.momentum == 0.0:
# Update on a per row basis, skip all-zero rows
for row in range(num_rows):
grad_row = grad[row].asnumpy()
all_zeros = mx.test_utils.almost_equal(grad_row, np.zeros_like(grad_row))
if all_zeros:
continue
if self.clip_gradient is not None:
weight[row] = ((1 - lr*wd)*weight[row] -
lr*mx.nd.clip(grad[row]*self.rescale_grad,
-self.clip_gradient, self.clip_gradient))
else:
weight[row] = (1 - lr*wd)*weight[row] - lr*self.rescale_grad*grad[row]
else:
mom = state
for row in range(num_rows):
grad_row = grad[row].asnumpy()
all_zeros = mx.test_utils.almost_equal(grad_row, np.zeros_like(grad_row))
if all_zeros:
continue
if self.clip_gradient is not None:
mom[row] = (self.momentum*mom[row] - lr*wd*weight[row] -
lr*mx.nd.clip(grad[row]*self.rescale_grad, -self.clip_gradient, self.clip_gradient))
weight[row] += mom[row]
else:
mom[row] = self.momentum*mom[row] - lr*wd*weight[row] - lr*self.rescale_grad*grad[row]
weight[row] += mom[row]
@with_seed()
def test_sparse_sgd():
opt1 = PySparseSGD
opt2 = mx.optimizer.SGD
shape = (3, 4, 5)
mom_options = [{}, {'momentum': 0.9}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
mp_options = [{}, {'multi_precision': False}, {'multi_precision': True}]
for dtype in [np.float32]:
for mom_option in mom_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in mp_options:
kwarg = {}
kwarg.update(mom_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype,
w_stype='row_sparse', g_stype='row_sparse')
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype,
w_stype='default', g_stype='row_sparse')
@with_seed()
def test_std_sparse_sgd():
opt1 = PySGD
opt2 = mx.optimizer.SGD
shape = (3, 4, 5)
mom_options = [{'momentum': 0.0}, {'momentum': 0.9}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
for dtype in [np.float32]:
for mom_option in mom_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
kwarg = {}
kwarg.update(mom_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
compare_optimizer(opt1(**kwarg), opt2(lazy_update=False, **kwarg), shape, dtype,
w_stype='row_sparse', g_stype='row_sparse')
compare_optimizer(opt1(**kwarg), opt2(lazy_update=False, **kwarg), shape, dtype,
w_stype='default', g_stype='row_sparse')
class PyNAG(PySGD):
def __init__(self, **kwargs):
super(PyNAG, self).__init__(**kwargs)
def create_state(self, index, weight):
"""Create additional optimizer state: momentum
Parameters
----------
weight : NDArray
The weight data
"""
momentum = None
weight_master_copy = None
do_multi_precision = self.multi_precision and weight.dtype == np.float16
if do_multi_precision:
if self.momentum != 0.0:
momentum = mx.nd.zeros(weight.shape, weight.context, dtype=np.float32)
weight_master_copy = array(weight, ctx=weight.context, dtype=np.float32)
return (weight_master_copy, momentum)
else:
if self.momentum != 0.0:
momentum = mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)
return momentum
def create_state_multi_precision(self, index, weight):
return self.create_state(index, weight)
def update(self, index, weight, grad, state):
"""Update the parameters.
Parameters
----------
index : int
An unique integer key used to index the parameters
weight : NDArray
weight ndarray
grad : NDArray
grad ndarray
state : NDArray or other objects returned by init_state
The auxiliary state used in optimization.
"""
lr = self._get_lr(index)
wd = self._get_wd(index)
self._update_count(index)
use_multi_precision = isinstance(state, list) or isinstance(state, tuple)
if not use_multi_precision:
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = mx.nd.clip(grad, -self.clip_gradient, self.clip_gradient)
if self.momentum == 0.0:
weight[:] += -lr * (grad + wd * weight)
else:
mom = state
mom[:] *= self.momentum
grad += wd * weight
mom[:] += grad
grad[:] += self.momentum * mom
weight[:] += -lr * grad
else:
grad32 = array(grad, ctx=grad.context, dtype=np.float32)
grad32 = grad32 * self.rescale_grad
if self.clip_gradient is not None:
grad32 = mx.nd.clip(grad32, -self.clip_gradient, self.clip_gradient)
mom = state[1]
weight32 = state[0]
if self.momentum == 0.0:
weight32[:] += -lr * (grad32 + wd * weight32)
else:
mom[:] *= self.momentum
grad32 += wd * weight32
mom[:] += grad32
grad32[:] += self.momentum * mom
weight32[:] += -lr * grad32
tmp = weight32.astype(weight.dtype)
tmp.copyto(weight)
@with_seed()
def test_nag():
opt1 = PyNAG
opt2 = mx.optimizer.NAG
shape = (3, 4, 5)
mom_options = [{}, {'momentum': 0.9}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
mp_options = [{}, {'multi_precision': False}, {'multi_precision': True}]
for dtype in [np.float16, np.float32, np.float64]:
for mom_option in mom_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in mp_options:
kwarg = {}
kwarg.update(mom_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
if (dtype == np.float16 and
('multi_precision' not in kwarg or
not kwarg['multi_precision'])):
continue
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype)
# FTML
class PyFTML(mx.optimizer.Optimizer):
"""python reference implemenation of FTML"""
def __init__(self, beta1=0.6, beta2=0.999, epsilon=1e-8, **kwargs):
super(PyFTML, self).__init__(**kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
def create_state(self, index, weight):
return (mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype), # d_0
mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype), # v_0
mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)) # z_0
def update(self, index, weight, grad, state):
assert(isinstance(weight, mx.nd. NDArray))
assert(isinstance(grad, mx.nd.NDArray))
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
t = self._index_update_count[index]
grad = grad * self.rescale_grad + wd * weight
if self.clip_gradient is not None:
grad = mx.nd.clip(grad, -self.clip_gradient, self.clip_gradient)
# get previous states
prev_d, prev_v, prev_z = state
# compute states
v_t = self.beta2 * prev_v + (1 - self.beta2) * mx.nd.square(grad)
d_t = (1 - pow(self.beta1, t)) / lr * (mx.nd.sqrt(v_t / (1 - pow(self.beta2, t))) + self.epsilon)
sigma_t = d_t - self.beta1 * prev_d
z_t = self.beta1 * prev_z + (1 - self.beta1) * grad - sigma_t * weight
# update weight
weight[:] = - z_t / d_t
# update states
prev_d[:] = d_t
prev_v[:] = v_t
prev_z[:] = z_t
@with_seed()
def test_ftml():
opt1 = PyFTML
opt2 = mx.optimizer.FTML
shape = (3, 4, 5)
beta1_options = [{}, {'beta1': 0.5}, {'beta1': 0.7}]
beta2_options = [{}, {'beta2': 0.8}, {'beta2': 0.9}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
for dtype in [np.float32]:
for beta1_option in beta1_options:
for beta2_option in beta2_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
kwarg = {}
kwarg.update(beta1_option)
kwarg.update(beta2_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype, rtol=1e-3, atol=1e-4)
# ADAM
class PyAdam(mx.optimizer.Optimizer):
"""python reference implemenation of adam"""
def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
decay_factor=(1 - 1e-8), lazy_update=True, **kwargs):
super(PyAdam, self).__init__(learning_rate=learning_rate, **kwargs)
self.beta1 = beta1
self.beta2 = beta2
self.epsilon = epsilon
self.decay_factor = decay_factor
self.lazy_update = lazy_update
def create_state(self, index, weight):
"""Create additional optimizer state: mean, variance
Parameters
----------
weight : NDArray
The weight data
"""
return (mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype), # mean
mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)) # variance
def update(self, index, weight, grad, state):
"""Update the parameters.
Parameters
----------
index : int
An unique integer key used to index the parameters
weight : NDArray
weight ndarray
grad : NDArray
grad ndarray
state : NDArray or other objects returned by init_state
The auxiliary state used in optimization.
"""
lr = self._get_lr(index)
self._update_count(index)
t = self._index_update_count[index]
mean, variance = state
wd = self._get_wd(index)
num_rows = weight.shape[0]
coef1 = 1. - self.beta1**t
coef2 = 1. - self.beta2**t
lr *= math.sqrt(coef2)/coef1
for row in range(num_rows):
# check row slices of all zeros
all_zeros = mx.test_utils.almost_equal(grad[row].asnumpy(), np.zeros_like(grad[row].asnumpy()))
# skip zeros during lazy update
if all_zeros and self.lazy_update:
continue
grad[row] = grad[row] * self.rescale_grad + wd * weight[row]
# clip gradients
if self.clip_gradient is not None:
mx.nd.clip(grad[row], -self.clip_gradient, self.clip_gradient, out=grad[row])
# update mean
mean[row] *= self.beta1
mean[row] += grad[row] * (1. - self.beta1)
# update variance
variance[row] *= self.beta2
variance[row] += (1 - self.beta2) * mx.nd.square(grad[row], out=grad[row])
# update weight
weight[row] -= lr*mean[row]/(mx.nd.sqrt(variance[row]) + self.epsilon)
@with_seed()
def test_adam():
opt1 = PyAdam
opt2 = mx.optimizer.Adam
shape = (3, 4, 5)
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
mp_options = [{}, {'multi_precision': False}, {'multi_precision': True}]
for dtype in [np.float16, np.float32, np.float64]:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in mp_options:
kwarg = {}
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
if (dtype == np.float16 and
('multi_precision' not in kwarg or
not kwarg['multi_precision'])):
continue
# atol 2e-5 needed to pass with seed 1248389097
compare_optimizer(opt1(lazy_update=False, **kwarg), opt2(**kwarg), shape, dtype,
rtol=1e-4, atol=2e-5)
# atol 2e-5 needed to pass with seed 781809840
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape,
dtype, w_stype='row_sparse', g_stype='row_sparse',
rtol=1e-4, atol=2e-5)
compare_optimizer(opt1(lazy_update=False, **kwarg), opt2(lazy_update=False, **kwarg), shape,
dtype, w_stype='row_sparse', g_stype='row_sparse',
rtol=1e-4, atol=2e-5)
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape,
dtype, w_stype='default', g_stype='row_sparse',
rtol=1e-4, atol=2e-5)
compare_optimizer(opt1(lazy_update=False, **kwarg), opt2(lazy_update=False, **kwarg), shape,
dtype, w_stype='default', g_stype='row_sparse',
rtol=1e-4, atol=2e-5)
# Signum
class PySignum(mx.optimizer.Optimizer):
"""The python reference of Signum optimizer.
The optimizer updates the weight by:
rescaled_grad = rescale_grad * clip(grad, clip_gradient) + wd * weight
state = momentum * state + (1-momentum)*rescaled_grad
weight = (1 - lr * wd_lh) * weight - lr * sign(state)
See the original paper at: https://jeremybernste.in/projects/amazon/signum.pdf
For details of the update algorithm see
:class:`~mxnet.ndarray.signsgd_update` and :class:`~mxnet.ndarray.signum_update`.
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
momentum : float, optional
The momentum value.
wd_lh : float, optitional
The amount of decoupled weight decay regularization.
"""
def __init__(self, learning_rate=0.01, momentum=0.9, wd_lh = 0.0, **kwargs):
super(PySignum, self).__init__(learning_rate = learning_rate, **kwargs)
self.momentum = momentum
self.wd_lh = wd_lh
def create_state(self, index, weight):
momentum = None
if self.momentum != 0.0:
momentum = mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype)
return momentum
def update(self, index, weight, grad, state):
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
if state is not None:
mom = state
if self.clip_gradient is not None:
mom[:] = (self.momentum*mom - (1-self.momentum)*(wd*weight +
mx.nd.clip(grad*self.rescale_grad, -self.clip_gradient, self.clip_gradient)))
else:
mom[:] = self.momentum*mom - (1-self.momentum)*wd*weight - (1-self.momentum)*self.rescale_grad*grad
weight[:] = (1 - lr*self.wd_lh)*weight + lr*mx.nd.sign(mom)
else:
weight[:] = (1 - lr*(wd+self.wd_lh))*weight - lr*mx.nd.sign(grad)
@with_seed()
def test_signum():
opt1 = PySignum
opt2 = mx.optimizer.Signum
shape = (3, 4, 5)
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
wd_lh_options = [{}, {'wd_lh': 0.015}, {'wd_lh': 0.0}]
mom_options = [{}, {'momentum': 0.9}]
lr_options = [{'learning_rate': 0.05},{'learning_rate': 0.01}]
for dtype in [np.float32, np.float64]:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in wd_lh_options:
for lr_option in lr_options:
for mom_option in mom_options:
kwarg = {}
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
kwarg.update(lr_option)
kwarg.update(mom_option)
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype)
# RMSProp
class PyRMSProp(mx.optimizer.Optimizer):
"""RMSProp optimizer of Tieleman & Hinton, 2012,
For centered=False, the code follows the version in
http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf by
Tieleman & Hinton, 2012
For centered=True, the code follows the version in
http://arxiv.org/pdf/1308.0850v5.pdf Eq(38) - Eq(45) by Alex Graves, 2013.
Parameters
----------
learning_rate : float, optional
Step size.
Default value is set to 0.001.
gamma1: float, optional
decay factor of moving average for gradient, gradient^2.
Default value is set to 0.9.
gamma2: float, optional
"momentum" factor.
Default value if set to 0.9.
Only used if centered=True
epsilon : float, optional
Default value is set to 1e-8.
centered : boolean, optional
Use Graves or Tielemans & Hintons version of RMSProp
wd : float, optional
L2 regularization coefficient add to all the weights
rescale_grad : float, optional
rescaling factor of gradient.
clip_gradient : float, optional
clip gradient in range [-clip_gradient, clip_gradient]
clip_weights : float, optional
clip weights in range [-clip_weights, clip_weights]
"""
def __init__(self, learning_rate=0.001, gamma1=0.9, gamma2=0.9,
epsilon=1e-8, centered=False, clip_weights=None, **kwargs):
super(PyRMSProp, self).__init__(learning_rate=learning_rate, **kwargs)
self.centered = centered
self.gamma1 = gamma1
self.gamma2 = gamma2
self.epsilon = epsilon
self.clip_weights = clip_weights
def create_state(self, index, weight):
"""Create additional optimizer state.
For centered=False: n
For centered=True: n, g, delta
Parameters
----------
weight : NDArray
The weight data
"""
if self.centered:
return (mx.nd.zeros(weight.shape, weight.context), # n
mx.nd.zeros(weight.shape, weight.context), # g
mx.nd.zeros(weight.shape, weight.context)) # delta
else:
return (mx.nd.zeros(weight.shape, weight.context), ) # n
def update(self, index, weight, grad, state):
"""Update the parameters.
Parameters
----------
index : int
An unique integer key used to index the parameters
weight : NDArray
weight ndarray
grad : NDArray
grad ndarray
state : NDArray or other objects returned by init_state
The auxiliary state used in optimization.
"""
lr = self._get_lr(index)
wd = self._get_wd(index)
self._update_count(index)
grad = grad * self.rescale_grad + wd * weight
if not self.centered:
(n, ) = state
if self.clip_gradient is not None:
grad = mx.nd.clip(grad, -self.clip_gradient, self.clip_gradient)
n[:] = (1 - self.gamma1) * (grad * grad) + self.gamma1 * n
weight[:] -= lr * grad/(mx.nd.sqrt(n + self.epsilon))
else:
n, g, delta = state
if self.clip_gradient is not None:
grad = mx.nd.clip(grad, -self.clip_gradient, self.clip_gradient)
n[:] = (1 - self.gamma1) * (grad * grad) + self.gamma1 * n
g[:] = (1 - self.gamma1) * grad + self.gamma1 * g
delta[:] = (self.gamma2) * delta - lr * grad/(mx.nd.sqrt(n - g*g + self.epsilon))
weight[:] += delta
if self.clip_weights:
mx.ndarray.clip(weight, -self.clip_weights, self.clip_weights, out=weight)
@with_seed()
def test_rms():
opt1 = PyRMSProp
opt2 = mx.optimizer.RMSProp
shape = (3, 4, 5)
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
cw_options = [{}, {'clip_weights': 0.01}]
center_options = [{}, {'centered': False}, {'centered': True}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.03}, {'wd': 0.05}, {'wd': 0.07}]
mp_options = [{}, {'multi_precision': False}, {'multi_precision': True}]
for dtype in [np.float16, np.float32]:
# Reduce foating point compare tolerance to avoid flaky test failure.
rtol, atol = (1e-1, 1e-1) if dtype is np.float16 else (1e-2, 1e-2)
for cw_option in cw_options:
for cg_option in cg_options:
for center_option in center_options:
for rg_option in rg_options:
for wd_option in wd_options:
for mp_option in mp_options:
kwarg = {}
kwarg.update(cw_option)
kwarg.update(cg_option)
kwarg.update(center_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
kwarg.update(mp_option)
if (dtype == np.float16 and
('multi_precision' not in kwarg or
not kwarg['multi_precision'])):
continue
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype, rtol=rtol, atol=atol)
if (default_context() == mx.cpu()):
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype, g_stype='row_sparse', rtol=rtol, atol=atol)
class PyFtrl(mx.optimizer.Optimizer):
"""The Ftrl optimizer.
Referenced from *Ad Click Prediction: a View from the Trenches*, available at
http://dl.acm.org/citation.cfm?id=2488200.
Parameters
----------
lamda1 : float, optional
L1 regularization coefficient.
learning_rate : float, optional
The initial learning rate.
beta : float, optional
Per-coordinate learning rate correlation parameter.
eta :
.. math::
\\eta_{t,i} = \\frac{learningrate}{\\beta+\\sqrt{\\sum_{s=1}^tg_{s,i}^t}}
"""
def __init__(self, lamda1=0.01, learning_rate=0.1, beta=1, lazy_update=False, **kwargs):
super(PyFtrl, self).__init__(**kwargs)
self.lamda1 = lamda1
self.beta = beta
self.lr = learning_rate
self.lazy_update = lazy_update
def create_state(self, index, weight):
return (mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype), # dn
mx.nd.zeros(weight.shape, weight.context, dtype=weight.dtype)) # n
def update(self, index, weight, grad, state):
self._update_count(index)
wd = self._get_wd(index)
lr = self._get_lr(index)
num_rows = weight.shape[0]
dn, n = state
for row in range(num_rows):
all_zeros = mx.test_utils.almost_equal(grad[row].asnumpy(), np.zeros_like(grad[row].asnumpy()))
if all_zeros and self.lazy_update:
continue
grad[row] = grad[row] * self.rescale_grad
if self.clip_gradient is not None:
mx.nd.clip(grad[row], -self.clip_gradient, self.clip_gradient, out=grad[row])
#update dn, n
dn[row] += grad[row] - (mx.nd.sqrt(n[row] + grad[row] * grad[row]) - mx.nd.sqrt(n[row])) * weight[row] / lr
n[row] += grad[row] * grad[row]
# update weight
weight[row] = (mx.nd.sign(dn[row]) * self.lamda1 - dn[row]) / \
((self.beta + mx.nd.sqrt(n[row])) / lr + wd) * (mx.nd.abs(dn[row]) > self.lamda1)
@with_seed()
def test_ftrl():
opt1 = PyFtrl
opt2 = mx.optimizer.Ftrl
shape = (3, 4, 5)
kwargs = [{},
{'clip_gradient': 0.5},
{'clip_gradient': 0.4, 'rescale_grad': 0.14},
{'rescale_grad': 0.8},
{'clip_gradient': 0.5, 'wd': 0.07},
{'clip_gradient': 0.4, 'rescale_grad': 0.14, 'wd': 0.03},
{'rescale_grad': 0.8, 'wd': 0.05},
{'rescale_grad': 0.8, 'wd': 0.05, 'lamda1': 0.01},
{'clip_gradient': 0.5, 'wd': 0.07, 'lamda1': 1.0}]
for kwarg in kwargs:
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, np.float32)
compare_optimizer(opt1(lazy_update=True, **kwarg), opt2(**kwarg), shape,
np.float32, w_stype='row_sparse', g_stype='row_sparse')
@with_seed()
def test_nadam():
def get_net(num_hidden, flatten=True):
data = mx.symbol.Variable('data')
fc1 = mx.symbol.FullyConnected(data, name='fc1', num_hidden=128, flatten=flatten)
act1 = mx.symbol.Activation(fc1, name='relu1', act_type="relu")
fc2 = mx.symbol.FullyConnected(act1, name = 'fc2', num_hidden = 64, flatten=flatten)
act2 = mx.symbol.Activation(fc2, name='relu2', act_type="relu")
fc3 = mx.symbol.FullyConnected(act2, name='fc3', num_hidden=num_hidden, flatten=flatten)
return fc3
N = 20
data = mx.random.uniform(-1, 1, shape=(N, 10))
label = mx.random.uniform(-1, 1, shape=(N, 1))
data_iter = mx.io.NDArrayIter(data, label, batch_size=5, label_name='label', shuffle=True)
output = get_net(1)
l = mx.symbol.Variable('label')
Loss = gluon.loss.L1Loss()
loss = Loss(output, l)
loss = mx.sym.make_loss(loss)
mod = mx.mod.Module(loss, data_names=('data',), label_names=('label',))
mod.fit(data_iter, num_epoch=60, optimizer_params={'learning_rate': 0.001, 'wd': 0.0005},
initializer=mx.init.Xavier(magnitude=2), eval_metric=mx.metric.Loss(),
optimizer='nadam')
assert mod.score(data_iter, eval_metric=mx.metric.Loss())[0][1] < 0.11
# AdaGrad
class PyAdaGrad(mx.optimizer.Optimizer):
"""The python reference of AdaGrad optimizer.
This class implements the AdaGrad optimizer described in *Adaptive Subgradient
Methods for Online Learning and Stochastic Optimization*, and available at
http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf.
Updates are applied by::
rescaled_grad = clip(grad * rescale_grad + wd * weight, clip_gradient)
history = history + square(rescaled_grad)
w = w - learning_rate * rescaled_grad / sqrt(history + epsilon)
This optimizer accepts the following parameters in addition to those accepted
by :class:`.Optimizer`.
Parameters
----------
eps: float, optional
Small value to avoid division by 0.
"""
def __init__(self, eps=1e-7, **kwargs):
super(PyAdaGrad, self).__init__(**kwargs)
self.float_stable_eps = eps
def create_state(self, index, weight):
return mx.nd.zeros(weight.shape, weight.context, stype=weight.stype)
def update(self, index, weight, grad, state):
self._update_count(index)
lr = self._get_lr(index)
wd = self._get_wd(index)
history = state
grad = grad * self.rescale_grad
if self.clip_gradient is not None:
grad = mx.nd.clip(grad, -self.clip_gradient, self.clip_gradient)
history[:] += mx.nd.square(grad)
div = grad / mx.nd.sqrt(history + self.float_stable_eps)
weight[:] += (div + weight * wd) * -lr
def test_adagrad():
mx.random.seed(0)
opt1 = PyAdaGrad
opt2 = mx.optimizer.AdaGrad
shape = (3, 4, 5)
eps_options = [{}, {'eps': 1e-8}]
cg_options = [{}, {'clip_gradient': 0.4}, {'clip_gradient': 0.5}]
rg_options = [{}, {'rescale_grad': 0.14}, {'rescale_grad': 0.8}]
wd_options = [{}, {'wd': 0.0}]
for dtype in [np.float32]:
for eps_option in eps_options:
for cg_option in cg_options:
for rg_option in rg_options:
for wd_option in wd_options:
kwarg = {}
kwarg.update(eps_option)
kwarg.update(cg_option)
kwarg.update(rg_option)
kwarg.update(wd_option)
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype)
if wd_option.get('wd', 0.0) == 0.0:
compare_optimizer(opt1(**kwarg), opt2(**kwarg), shape, dtype,