-
Notifications
You must be signed in to change notification settings - Fork 176
/
xor_mlp_td.py
319 lines (296 loc) · 14.4 KB
/
xor_mlp_td.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
#!/usr/bin/env python
#MIT License
#Copyright (c) 2017 Massimiliano Patacchiola
#
#Permission is hereby granted, free of charge, to any person obtaining a copy
#of this software and associated documentation files (the "Software"), to deal
#in the Software without restriction, including without limitation the rights
#to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
#copies of the Software, and to permit persons to whom the Software is
#furnished to do so, subject to the following conditions:
#
#The above copyright notice and this permission notice shall be included in all
#copies or substantial portions of the Software.
#
#THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
#IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
#FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
#AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
#LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
#OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
#SOFTWARE.
#In this example I will use the class gridworld to generate a 5x5 world
#in which the cleaning robot will move. Rewards are allocated in the 4
#corners of the world following the XOR pattern. I will use an function
#approximator based on a paraboloid-like function in order to represent
#a TD(0) function approximator.
import numpy as np
from gridworld import GridWorld
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.animation as animation
from matplotlib.patches import Rectangle
import mpl_toolkits.mplot3d.art3d as art3d
from matplotlib import cm
from mlp import MLP
def init_env():
'''Init the XOR boolean environment
@return the environment gridworld object
'''
env = GridWorld(5, 5)
#Define the state matrix
state_matrix = np.array([[1.0, 0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[1.0, 0.0, 0.0, 0.0, 1.0]])
#Define the index matrix
index_matrix = np.array([[(4,0), (4,1), (4,2), (4,3), (4,4)],
[(3,0), (3,1), (3,2), (3,3), (3,4)],
[(2,0), (2,1), (2,2), (2,3), (2,4)],
[(1,0), (1,1), (1,2), (1,3), (1,4)],
[(0,0), (0,1), (0,2), (0,3), (0,4)]])
#Define the reward matrix
reward_matrix = np.array([[1.0, 0.0, 0.0, 0.0, -1.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 0.0, 0.0, 0.0, 0.0],
[-1.0, 0.0, 0.0, 0.0, 1.0]])
#Define the transition matrix
transition_matrix = np.array([[0.8, 0.1, 0.0, 0.1],
[0.1, 0.8, 0.1, 0.0],
[0.0, 0.1, 0.8, 0.1],
[0.1, 0.0, 0.1, 0.8]])
env.setStateMatrix(state_matrix)
env.setIndexMatrix(index_matrix)
env.setRewardMatrix(reward_matrix)
env.setTransitionMatrix(transition_matrix)
return env
def update(my_mlp, new_observation, reward, learning_rate, gamma, done):
'''Return the updated weights vector w_t1
@param w the weights vector before the update
@param x the feauture vector obsrved at t
@param x_t1 the feauture vector observed at t+1
@param reward the reward observed after the action
@param gamma the discount factor
@param done boolean True if the state is terminal
@return w_t1 the weights vector at t+1
'''
if done:
x = np.array(new_observation, dtype=np.float32)
target = np.array([reward], dtype=np.float32)
#print(target)
error = my_mlp.train(x, target, learning_rate)
else:
x = np.array(new_observation, dtype=np.float32)
target = np.array((reward + (gamma * my_mlp.forward(x))), dtype=np.float32)
#print target
error = my_mlp.train(x, target, learning_rate)
return my_mlp, error
def print_utility(my_mlp, tot_rows, tot_cols, decimal=2, flip=True):
'''Print on terminal the utility matrix of a discrete state space
having states defined by tuples: (0,0); (0,1); (0,2) ...
@param my_mlp an MLP object having single output
@param tot_rows total number of rows
@param tot_cols total number of columns
@param decimal is the precision of the printing (default: 2 decimal places)
@param flip boolean which defines if vertical flip is applied (default: True)
'''
utility_matrix = np.zeros((tot_rows, tot_cols))
for row in range(tot_rows):
for col in range(tot_cols):
x = np.array([row, col], dtype=np.float32)
utility_matrix[row,col] = my_mlp.forward(x)
np.set_printoptions(precision=decimal) #set print precision of numpy
if flip:
print(np.flipud(utility_matrix))
else:
print(utility_matrix)
np.set_printoptions(precision=8) #reset to default
def subplot(my_mlp, world_size, filename="figure.png"):
#Define the main figure property
fig, ax = plt.subplots(nrows=1, ncols=4, subplot_kw={'projection': '3d', 'autoscale_on':False, 'aspect':'equal'})
#XOR color
color_00 = "red"
color_11 = "red"
color_10 = "green"
color_01 = "green"
#Quadratic subplot
ax[0].clear()
#Draw the rectangles
p = Rectangle((0, 0), 1, 1, color=color_00, alpha=0.5)
ax[0].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, world_size-1), 1, 1, color=color_11, alpha=0.5)
ax[0].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((0, world_size-1), 1, 1, color=color_01, alpha=0.5)
ax[0].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, 0), 1, 1, color=color_10, alpha=0.5)
ax[0].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
#Set the plot
ax[0].set_xticks(np.arange(0, world_size+1, 1))
ax[0].set_xticklabels('', fontsize=10)
ax[0].set_yticklabels('', fontsize=10)
ax[0].set_yticks(np.arange(0, world_size+1, 1))
ax[0].set_zlim(-1.0,1.0)
#ax[0].set_zticklabels(['-1.0','','0','','1.0'], fontsize=10)
ax[0].view_init(elev=30, azim=-115)
x, y = np.meshgrid(np.arange(0.0, world_size-1.0, 0.01), np.arange(0.0, world_size-1.0, 0.01))
grid = np.arange(0.0, world_size-1.0, 0.01)
z_matrix = list()
for x_i in grid:
z_row = list()
for y_i in grid:
z_row.append(my_mlp.forward(np.array([x_i, y_i])))
z_matrix.append(z_row)
z = np.squeeze(np.array(z_matrix))
ax[0].plot_surface(x+0.5,y+0.5,z, color='lightgrey', alpha=0.5, linewidth=0, antialiased=False) # color='lightgrey', alpha=0.5)
#Draw a White background
x, y = np.meshgrid(np.arange(0, world_size+1, 1), np.arange(0, world_size+1, 1))
z = x*(-1.0)
ax[0].plot_surface(x,y,z, color='white', alpha=0.01)
#Quadratic subplot
ax[1].clear()
#Draw the rectangles
p = Rectangle((0, 0), 1, 1, color=color_00, alpha=0.5)
ax[1].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, world_size-1), 1, 1, color=color_11, alpha=0.5)
ax[1].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((0, world_size-1), 1, 1, color=color_01, alpha=0.5)
ax[1].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, 0), 1, 1, color=color_10, alpha=0.5)
ax[1].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
#Set the plot
ax[1].set_xticks(np.arange(0, world_size+1, 1))
ax[1].set_xticklabels('', fontsize=10)
ax[1].set_yticklabels('', fontsize=10)
ax[1].set_yticks(np.arange(0, world_size+1, 1))
ax[1].set_zlim(-1.0,1.0)
ax[1].set_zticklabels([''], fontsize=10)
ax[1].view_init(elev=30, azim=-65)
x, y = np.meshgrid(np.arange(0.0, world_size-1.0, 0.01), np.arange(0.0, world_size-1.0, 0.01))
grid = np.arange(0.0, world_size-1.0, 0.01)
z_matrix = list()
for x_i in grid:
z_row = list()
for y_i in grid:
z_row.append(my_mlp.forward(np.array([x_i, y_i])))
z_matrix.append(z_row)
z = np.squeeze(np.array(z_matrix))
ax[1].plot_surface(x+0.5,y+0.5,z, color='lightgrey', alpha=0.5, linewidth=0, antialiased=False) # color='lightgrey', alpha=0.5)
#Draw a White background
x, y = np.meshgrid(np.arange(0, world_size+1, 1), np.arange(0, world_size+1, 1))
z = x*(-1.0)
ax[1].plot_surface(x,y,z, color='white', alpha=0.01)
#Quadratic subplot
ax[2].clear()
#Draw the rectangles
p = Rectangle((0, 0), 1, 1, color=color_00, alpha=0.5)
ax[2].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, world_size-1), 1, 1, color=color_11, alpha=0.5)
ax[2].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((0, world_size-1), 1, 1, color=color_01, alpha=0.5)
ax[2].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, 0), 1, 1, color=color_10, alpha=0.5)
ax[2].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
#Set the plot
ax[2].set_xticks(np.arange(0, world_size+1, 1))
ax[2].set_xticklabels('', fontsize=10)
ax[2].set_yticklabels('', fontsize=10)
ax[2].set_yticks(np.arange(0, world_size+1, 1))
ax[2].set_zlim(-1.0,1.0)
ax[2].set_zticklabels([''], fontsize=10)
ax[2].view_init(elev=30, azim=-45)
x, y = np.meshgrid(np.arange(0.0, world_size-1.0, 0.01), np.arange(0.0, world_size-1.0, 0.01))
grid = np.arange(0.0, world_size-1.0, 0.01)
z_matrix = list()
for x_i in grid:
z_row = list()
for y_i in grid:
z_row.append(my_mlp.forward(np.array([x_i, y_i])))
z_matrix.append(z_row)
z = np.squeeze(np.array(z_matrix))
ax[2].plot_surface(x+0.5,y+0.5,z, color='lightgrey', alpha=0.5, linewidth=0, antialiased=False) # color='lightgrey', alpha=0.5)
#Draw a White background
x, y = np.meshgrid(np.arange(0, world_size+1, 1), np.arange(0, world_size+1, 1))
z = x*(-1.0)
ax[2].plot_surface(x,y,z, color='white', alpha=0.01)
#Quadratic subplot
ax[3].clear()
#Draw the rectangles
p = Rectangle((0, 0), 1, 1, color=color_00, alpha=0.5)
ax[3].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, world_size-1), 1, 1, color=color_11, alpha=0.5)
ax[3].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((0, world_size-1), 1, 1, color=color_01, alpha=0.5)
ax[3].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
p = Rectangle((world_size-1, 0), 1, 1, color=color_10, alpha=0.5)
ax[3].add_patch(p)
art3d.pathpatch_2d_to_3d(p, z=-1.0, zdir="z")
#Set the plot
ax[3].set_xticks(np.arange(0, world_size+1, 1))
ax[3].set_xticklabels('', fontsize=10)
ax[3].set_yticklabels('', fontsize=10)
ax[3].set_yticks(np.arange(0, world_size+1, 1))
ax[3].set_zlim(-1.0,1.0)
ax[3].set_zticklabels([''], fontsize=10)
ax[3].view_init(elev=30, azim=-25)
x, y = np.meshgrid(np.arange(0.0, world_size-1.0, 0.01), np.arange(0.0, world_size-1.0, 0.01))
grid = np.arange(0.0, world_size-1.0, 0.01)
z_matrix = list()
for x_i in grid:
z_row = list()
for y_i in grid:
z_row.append(my_mlp.forward(np.array([x_i, y_i])))
z_matrix.append(z_row)
z = np.squeeze(np.array(z_matrix))
ax[3].plot_surface(x+0.5,y+0.5,z, color='lightgrey', alpha=0.5, linewidth=0, antialiased=False) # color='lightgrey', alpha=0.5)
#Draw a White background
x, y = np.meshgrid(np.arange(0, world_size+1, 1), np.arange(0, world_size+1, 1))
z = x*(-1.0)
ax[3].plot_surface(x,y,z, color='white', alpha=0.01)
#Save the figure
fig.tight_layout()
fig.savefig(filename, dpi=300) #, bbox_inches='tight')
def main():
env = init_env()
my_mlp = MLP(tot_inputs=2, tot_hidden=2, tot_outputs=1, activation="tanh")
learning_rate = 0.1
gamma = 0.9
tot_epoch = 10001
print_epoch = 100
for epoch in range(tot_epoch):
#XOR-world episode
observation = env.reset(exploring_starts=True)
#The episode starts here
for step in range(1000):
action = np.random.randint(0,4)
new_observation, reward, done = env.step(action) #move in the world and get the state and reward
my_mlp, error = update(my_mlp, new_observation, reward, learning_rate, gamma, done)
observation = new_observation
if done: break
if(epoch % print_epoch == 0 and epoch!=0):
print("")
print("Epoch: " + str(epoch+1))
print("Tot steps: " + str(step))
print("Error: " + str(error))
print_utility(my_mlp, tot_rows=5, tot_cols=5)
print("Generating plot, please wait...")
subplot(my_mlp, world_size=5, filename="xor_planes.png")
print("Done!")
if __name__ == "__main__":
main()