-
Notifications
You must be signed in to change notification settings - Fork 1
/
learn.py
587 lines (525 loc) · 20.9 KB
/
learn.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
'''
This file implements learning agents for the goal domain.
'''
import numpy as np
import pickle
from numpy.linalg import norm
from simulator import Simulator, keeper_line, angle_difference, keeper_target, norm_angle, bound
from random import choice
from util import angle_between, to_matrix, vector
from config import PITCH_LENGTH, PITCH_WIDTH, GOAL_WIDTH
import cma
def softmax(values):
''' Returns the softmax weighting of a set of values. '''
maxval = max(values)
values = [np.exp(value - maxval) for value in values]
total = sum(values)
return [value / total for value in values]
def weighted_selection(values):
''' Select an index with probabilities given by values. '''
rand = np.random.rand()
for index, value in enumerate(values):
if rand <= value:
return index
rand -= value
return 0
def keeper_projection(state):
if state[5] == state[10]:
if state[6] < state[11]:
return -GOAL_WIDTH/2
else:
return GOAL_WIDTH/2
grad = (state[6] - state[11]) / (state[5] - state[10])
y_int = state[11] - grad * state[10]
pos = grad * PITCH_LENGTH/2 + y_int
return bound(pos, -GOAL_WIDTH/2, GOAL_WIDTH)
def keeper_features(state):
''' Returns (1 g), where g is the projection
of the goalie onto the goal line. '''
yval = keeper_projection(state)
return np.array([1, yval])
FOURIER_DIM = 7
def generate_coefficients(coeffs, vector = np.zeros((14,)), depth = 0, count = 0):
''' Generate all coefficient vectors. '''
if depth == 14 or count == 2:
coeffs.append(vector)
else:
if depth in [3, 4, 7, 8, 12, 13]:
generate_coefficients(coeffs, vector, depth+1, count)
else:
for j in range(FOURIER_DIM):
new_vector = np.copy(vector)
new_vector[depth] = np.pi * j
generate_coefficients(coeffs, new_vector, depth+1, count + (j > 0))
SCALE_VECTOR = np.array([PITCH_LENGTH/2, PITCH_WIDTH, 2.0, 2.0,
2*np.pi, PITCH_LENGTH/2, PITCH_WIDTH, 2.0, 2.0, 2*np.pi, PITCH_LENGTH/2, PITCH_WIDTH, 6.0, 6.0])
SHIFT_VECTOR = np.array([0.0, PITCH_WIDTH/2, 1.0, 1.0, np.pi, 0.0, PITCH_WIDTH/2, 1.0, 1.0, np.pi, 0.0, PITCH_WIDTH/2, 3, 3 ])
COEFFS = []
generate_coefficients(COEFFS)
BASIS_COUNT = len(COEFFS)
COEFF_SCALE = np.ones(BASIS_COUNT)
print BASIS_COUNT
for i in range(1, BASIS_COUNT):
COEFF_SCALE[i] = norm(COEFFS[i])
def scale_state(state):
''' Scale state variables between 0 and 1. '''
new_state = np.copy(state)
return (new_state + SHIFT_VECTOR) / SCALE_VECTOR
def fourier_basis(state):
''' Defines a fourier basis function. '''
basis = np.zeros((BASIS_COUNT,))
scaled = scale_state(state)
for i, coeff in enumerate(COEFFS):
basis[i] = np.cos(coeff.dot(scaled))
return basis
def position_features(state):
''' Returns (1 p p^2), containing the squared features
of the player position. '''
xval = state[0] / (PITCH_LENGTH / 2)
yval = state[1] / (PITCH_WIDTH / 2)
return np.array([1, xval, yval, xval**2, yval**2])
def ball_features(state):
''' Returns ball-based position features. '''
ball = vector(state[10], state[11])
keeper = vector(state[5], state[6])
diff = (ball - keeper) / norm(ball - keeper)
return np.array([1, state[10], state[11], diff[0], diff[1]])
class Agent:
'''
Implements an agent with a parameterized or weighted policy.
'''
action_count = 3
temperature = 1.0
variance = 0.01
alpha = 0.1
gamma = 0.9
num = 100
action_features = [position_features, position_features, position_features]
parameter_features = [ball_features, keeper_features, keeper_features]
def __init__(self):
''' Sets up the parameterized policy. '''
self.action_weights = [
np.zeros((5,)),
np.zeros((5,)),
np.zeros((5,))]
xfear = 50.0/PITCH_LENGTH
yfear = 50.0/PITCH_WIDTH
caution = 5.0/PITCH_WIDTH
kickto_weights = np.array([[2.5, 1, 0, xfear, 0],[0, 0, 1 - caution, 0, yfear]]).T
self.parameter_weights = [
kickto_weights,
np.array([[GOAL_WIDTH/2 - 1, 0]]).T,
np.array([[-GOAL_WIDTH/2 + 1, 0]]).T]
def run_episode(self, simulator = None):
''' Run a single episode for a maximum number of steps. '''
if simulator == None:
simulator = Simulator()
state = simulator.get_state()
states = [state]
rewards = []
actions = []
acts = []
end_ep = False
while not end_ep:
act = self.action_policy(state)
action = self.policy(state, act)
state, reward, end_ep, _ = simulator.take_action(action)
states.append(state)
actions.append(action)
rewards.append(reward)
acts.append(act)
return states, actions, rewards, acts
def evaluate_policy(self, runs):
''' Evaluate the current policy. '''
average_reward = 0
for _ in range(runs):
rewards = self.run_episode()[2]
average_reward += sum(rewards) / runs
return average_reward
def policy(self, state, action = None):
''' Policy selects an action based on its internal policies. '''
if action == None:
action = self.action_policy(state)
parameters = self.parameter_policy(state, action)
if action != 0:
parameters = (parameters,)
action_names = ['kickto', 'shootgoal', 'shootgoal']
return (action_names[action], parameters)
def action_prob(self, state):
''' Computes the probability of selecting each action. '''
values = []
for i in range(self.action_count):
features = self.action_features[i](state)
val = self.action_weights[i].T.dot(features)
values.append(val / self.temperature)
return softmax(values)
def action_policy(self, state):
''' Selects an action based on action probabilities. '''
values = self.action_prob(state)
return weighted_selection(values)
def parameter_policy(self, state, action):
''' Computes the parameters for the given action. '''
features = self.parameter_features[action](state)
weights = self.parameter_weights[action]
mean = weights.T.dot(features)
if action == 0:
covariance = self.variance * np.eye(2)
return np.random.multivariate_normal(mean, covariance)
else:
return np.random.normal(mean, self.variance)
def get_parameters(self):
''' Returns all the parameters in a vector. '''
parameters = np.zeros((0,))
for action in range(self.action_count):
parameters = np.append(parameters, self.action_weights[action])
cols = self.parameter_weights[action].shape[1]
for col in range(cols):
parameters = np.append(parameters, self.parameter_weights[action][:, col])
return parameters
def set_parameters(self, parameters):
''' Set the parameters using a vector. '''
index = 0
for action in range(self.action_count):
size = self.action_weights[action].size
self.action_weights[action] = parameters[index: index+size]
index += size
rows, cols = self.parameter_weights[action].shape
for col in range(cols):
self.parameter_weights[action][:, col] = parameters[index: index+rows]
index += rows
def log_action_gradient(self, state, action, selection):
''' Returns the log gradient for action,
given the state and the selection used. '''
features = self.action_features[action](state)
prob = self.action_prob(state)[action]
if action == selection:
return (1 - prob)*features / self.temperature
else:
return - prob * features / self.temperature
def log_parameter_gradient(self, state, action, value, col):
''' Returns the log gradient for the parameter,
given the state and the col of values. '''
features = self.parameter_features[action](state)
mean = self.parameter_weights[action][:, col].dot(features)
grad = (value - mean) * features / self.variance
return grad
def log_gradient(self, state, action, value):
''' Returns the log gradient for the entire policy. '''
grad = np.zeros((0,))
for i in range(self.action_count):
action_grad = self.log_action_gradient(state, i, action)
grad = np.append(grad, action_grad)
rows, cols = self.parameter_weights[i].shape
if i == action:
for col in range(cols):
parameter_grad = self.log_parameter_gradient(state, i, value[col], col)
grad = np.append(grad, parameter_grad)
else:
grad = np.append(grad, np.zeros((rows*cols,)))
return grad
def update(self):
''' Perform one learning update. '''
pass
def learn(self, steps):
''' Learn for the given number of update steps. '''
returns = []
total = 0
for step in range(steps):
rets = self.update()
self.alpha *= (self.num + step) / (self.num + step + 1.0)
returns.extend(rets)
total += sum(rets)
print 'Step:', step, rets, total / (step + 1)
return returns
class FixedSarsaAgent(Agent):
''' A fixed parameter weight gradient-descent SARSA agent. '''
name = 'fixedsarsa'
colour = '-k'
legend = 'Fixed Sarsa'
alpha = 0.01
lmb = 0.1
action_features = [fourier_basis, fourier_basis, fourier_basis]
def __init__(self):
''' Initialize coeffs. '''
Agent.__init__(self)
for i in range(3):
self.action_weights[i] = np.zeros((BASIS_COUNT,))
def update(self):
''' Learn for a single episode. '''
simulator = Simulator()
state = simulator.get_state()
act = self.action_policy(state)
feat = self.action_features[act](state)
end_episode = False
traces = [
np.zeros((BASIS_COUNT,)),
np.zeros((BASIS_COUNT,)),
np.zeros((BASIS_COUNT,))]
while not end_episode:
action = self.policy(state, act)
state, reward, end_episode, _ = simulator.take_action(action)
new_act = self.action_policy(state)
new_feat = self.action_features[new_act](state)
delta = reward + self.gamma * self.action_weights[new_act].dot(new_feat) - self.action_weights[act].dot(feat)
for i in range(3):
traces[i] *= self.lmb * self.gamma
traces[act] += feat
for i in range(3):
self.action_weights[i] += self.alpha * delta * traces[i] / COEFF_SCALE
act = new_act
feat = new_feat
return [reward]
class CmaesAgent(Agent):
''' Defines a CMA-ES agent. '''
colour = 'r'
legend = 'CMA-ES'
name = 'cmaes'
runs = 5
sigma = 0.1
def objective_function(self, container, parameters):
''' Defines a simple objective function for direct optimization. '''
self.set_parameters(parameters)
total = 0
for _ in range(self.runs):
reward = self.evaluate_policy(1)
total -= reward / self.runs
container.append(reward)
return total
def learn(self, _):
''' Learn until convergence. '''
returns = []
function = lambda parameters: self.objective_function(returns, parameters)
res = cma.fmin(function, self.get_parameters(), self.sigma)
self.set_parameters(res[5])
return returns
class AlternatingAgent(FixedSarsaAgent):
''' Alternates learning using Sarsa and Cmaes. '''
colour = '--b'
legend = 'Alternating Optimization'
name = 'ao'
qsteps = 1000
runs = 5
sigma = 0.1
def objective_function(self, container, parameters):
''' Defines a simple objective function for direct optimization. '''
self.set_parameters(parameters)
total = 0
for _ in range(self.runs):
reward = self.evaluate_policy(1)
total -= reward / self.runs
container.append(reward)
return total
def get_parameters(self):
''' Get the parameter weights. '''
parameters = np.zeros((0,))
for action in range(self.action_count):
cols = self.parameter_weights[action].shape[1]
for col in range(cols):
parameters = np.append(parameters, self.parameter_weights[action][:, col])
return parameters
def set_parameters(self, parameters):
''' Set the parameters using a vector. '''
index = 0
for action in range(self.action_count):
rows, cols = self.parameter_weights[action].shape
for col in range(cols):
self.parameter_weights[action][:, col] = parameters[index: index+rows]
index += rows
def learn(self, steps):
''' Learn for a given number of steps. '''
returns = []
function = lambda parameters: self.objective_function(returns, parameters)
for step in range(steps):
agent = FixedSarsaAgent()
agent.action_weights = self.action_weights
agent.parameter_weights = self.parameter_weights
rets = agent.learn(self.qsteps)
returns.extend(rets)
res = cma.fmin(function, self.get_parameters(), self.sigma)
self.set_parameters(res[5])
return returns
class QpamdpAgent(FixedSarsaAgent):
''' Defines an agen to optimize H(theta) using eNAC. '''
relearn = 50
runs = 50
name = 'qpamdp'
legend = 'Q-PAMDP(1)'
colour = '-.g'
beta = 0.1
num = 100
num2 = 1000
def get_parameters(self):
''' Get the parameter weights. '''
parameters = np.zeros((0,))
for action in range(self.action_count):
cols = self.parameter_weights[action].shape[1]
for col in range(cols):
parameters = np.append(parameters, self.parameter_weights[action][:, col])
return parameters
def set_parameters(self, parameters):
''' Set the parameters using a vector. '''
index = 0
for action in range(self.action_count):
rows, cols = self.parameter_weights[action].shape
for col in range(cols):
self.parameter_weights[action][:, col] = parameters[index: index+rows]
index += rows
def log_gradient(self, state, action, value):
''' Returns the log gradient for the entire policy. '''
grad = np.zeros((0,))
for i in range(self.action_count):
rows, cols = self.parameter_weights[i].shape
if i == action:
for col in range(cols):
parameter_grad = self.log_parameter_gradient(state, i, value[col], col)
grad = np.append(grad, parameter_grad)
else:
grad = np.append(grad, np.zeros((rows*cols,)))
return grad
def enac_gradient(self):
''' Compute the episodic NAC gradient. '''
returns = np.zeros((self.runs, 1))
phi = lambda state: np.array([1, state[1], state[1]**2])
param_size = self.get_parameters().size
psi = np.zeros((self.runs, param_size+3))
for run in range(self.runs):
states, actions, rewards, acts = self.run_episode()
returns[run, 0] = sum(rewards)
log_grad = np.zeros((param_size,))
for state, act, action in zip(states, acts, actions):
val = action[1]
log_grad += self.log_gradient(state, act, val)
psi[run, :] = np.append(log_grad, phi(states[0]))
omega_v = np.linalg.pinv(psi).dot(returns)
grad = omega_v[0:param_size, 0]
return grad, returns
def parameter_update(self):
''' Perform a single gradient update. '''
grad, returns = self.enac_gradient()
if norm(grad) > 0:
grad /= norm(grad)
self.set_parameters(self.get_parameters() + self.beta * grad)
return returns
def learn(self, steps):
''' Learn for a given number of steps. '''
returns = []
for step in range(2000):
new_ret = self.update()
print new_ret
returns.extend(new_ret)
for step in range(steps):
new_ret = self.parameter_update()
print new_ret
returns.extend(new_ret)
for update in range(self.relearn):
new_ret = self.update()
print new_ret
returns.extend(new_ret)
print step
return returns
class EnacAoAgent(QpamdpAgent):
''' Defines an alternating agent using eNAC. '''
name = 'enacao'
legend = 'Q-PAMDP($\infty$)'
colour = '--b'
def learn(self, steps):
''' Learn for a given number of steps. '''
returns = []
for step in range(2000):
new_ret = self.update()
print new_ret
returns.extend(new_ret)
for step in range(steps):
for i in range(1000):
new_ret = self.parameter_update()
print i, new_ret
returns.extend(new_ret)
for update in range(2000):
new_ret = self.update()
print new_ret
returns.extend(new_ret)
print step
return returns
class EnacAgent(QpamdpAgent):
''' Defines an agent to optimize J(theta, omega) using eNAC. '''
name = 'enac'
legend = 'eNAC'
colour = ':r'
def get_parameters(self):
''' Returns all the parameters in a vector. '''
parameters = np.zeros((0,))
for action in range(self.action_count):
parameters = np.append(parameters, self.action_weights[action])
cols = self.parameter_weights[action].shape[1]
for col in range(cols):
parameters = np.append(parameters, self.parameter_weights[action][:, col])
return parameters
def set_parameters(self, parameters):
''' Set the parameters using a vector. '''
index = 0
for action in range(self.action_count):
size = self.action_weights[action].size
self.action_weights[action] = parameters[index: index+size]
index += size
rows, cols = self.parameter_weights[action].shape
for col in range(cols):
self.parameter_weights[action][:, col] = parameters[index: index+rows]
index += rows
def log_gradient(self, state, action, value):
''' Returns the log gradient for the entire policy. '''
grad = np.zeros((0,))
for i in range(self.action_count):
action_grad = self.log_action_gradient(state, i, action)
grad = np.append(grad, action_grad)
rows, cols = self.parameter_weights[i].shape
if i == action:
for col in range(cols):
parameter_grad = self.log_parameter_gradient(state, i, value[col], col)
grad = np.append(grad, parameter_grad)
else:
grad = np.append(grad, np.zeros((rows*cols,)))
return grad
def learn(self, steps):
''' Learn for a given number of steps. '''
returns = []
for step in range(steps):
new_ret = self.parameter_update()
print new_ret
returns.extend(new_ret)
print step
return returns
def determine_variance(steps, runs = 1):
''' Determine the variance of parameterized policy agent. '''
agent = FixedSarsaAgent()
agent.learn(2000)
rewards = []
for _ in range(steps):
reward = agent.evaluate_policy(runs)
rewards.append(reward)
print reward
mean = sum(rewards) / steps
variance = 0
for reward in rewards:
variance += (reward - mean)**2 / steps
print
print 'Mean:', mean
print 'Variance:', variance
def save_run(agent_class, steps, run):
''' Save a single run. '''
agent = agent_class()
returns = np.array(agent.learn(steps))
np.save('./runs/'+agent.name+'/'+str(run), returns)
with file('./runs/'+agent.name+'/'+str(run)+'.obj', 'w') as file_handle:
pickle.dump(agent, file_handle)
def extend_run(agent_class, steps, run):
''' Extend an existing run for a given number of steps. '''
agent = None
with file('./runs/'+agent_class.name +'/'+str(run)+'.obj', 'r') as file_handle:
agent = pickle.load(file_handle)
run_name = './runs/'+agent.name+'/'+str(run)+'.npy'
returns = np.load(run_name)
returns = np.append(returns, agent.learn(steps))
np.save(run_name, returns)
if agent != None:
with file('./runs/'+agent_class.name +'/'+str(run)+'.obj', 'w') as file_handle:
pickle.dump(agent, file_handle)