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rl_maze_policy_grad.py
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# -*- coding: utf-8 -*-
"""RL_maze_Policy_Grad.ipynb
Automatically generated by Colaboratory.
Original file is located at
https://colab.research.google.com/drive/1TCqY1mzgdqXEpHkJV-fpN9Bo1czYrIIT
"""
# Commented out IPython magic to ensure Python compatibility.
# Modification from "https://github.com/YutaroOgawa/Deep-Reinforcement-Learning-Book/blob/master/program/2_2_maze_random.ipynb"
'''
Add Using Policy Gradient !!!
'''
import numpy as np
import matplotlib
matplotlib.use('Agg')
from matplotlib import animation, rc
matplotlib.rcParams['animation.embed_limit'] = 2**128
import matplotlib.pyplot as plt
# %matplotlib inline
# Initialize State of Maze
# Set the size of the Graph
fig = plt.figure( figsize=(10, 10) )
ax = plt.gca()
# Draw the Red Wall
# [x1, y1] ---> [x2, y2]
#plt.plot([x1, x2], [y1, y2], color='red', linewidth=2)
lwd=12
plt.plot([ 0, 0 ], [ 0, 10 ], color='red', linewidth=lwd)
plt.plot([ 0,10 ], [ 10, 10 ], color='red', linewidth=lwd)
plt.plot([ 10,10 ], [ 10, 0 ], color='red', linewidth=lwd)
plt.plot([ 10, 0 ], [ 0, 0 ], color='red', linewidth=lwd)
plt.plot([1, 1 ], [ 1, 1 + 7], color='red', linewidth=lwd)
plt.plot([1, 2 ], [ 2 + 7, 2 + 7], color='red', linewidth=lwd)
plt.plot([2, 2 ], [ 2 + 7, 1 + 7], color='red', linewidth=lwd)
plt.plot([2, 3 + 7], [ 1 + 7, 1 + 7], color='red', linewidth=lwd)
plt.plot([1, 3 ], [-1 + 7,-1 + 7], color='red', linewidth=lwd)
plt.plot([4, 9 ], [-1 + 7,-1 + 7], color='red', linewidth=lwd)
plt.plot([1, 9 ], [ 0 + 7, 0 + 7], color='red', linewidth=lwd)
plt.plot([2, 2 ], [ 0, -2 + 7], color='red', linewidth=lwd)
plt.plot([3, 3 ], [ 1, -1 + 7], color='red', linewidth=lwd)
plt.plot([4, 4 ], [ 0, -2 + 7], color='red', linewidth=lwd)
plt.plot([5, 5 ], [ 1, -1 + 7], color='red', linewidth=lwd)
plt.plot([6, 6 ], [ 0, -2 + 7], color='red', linewidth=lwd)
plt.plot([7, 7 ], [ 1, -1 + 7], color='red', linewidth=lwd)
plt.plot([8, 8 ], [ 0, -2 + 7], color='red', linewidth=lwd)
plt.plot([9, 9 ], [ 1, -1 + 7], color='red', linewidth=lwd)
plt.plot([3, 4 ], [ 5, 5 ], color='red', linewidth=lwd)
plt.plot([9, 10 ], [ 1, 1 ], color='red', linewidth=lwd)
# Draw the text to represent state of agent in the maze
def plot_fun(i,j):
plt.text(i+0.5, (9-j)+0.5, 'S_{}'.format(i + j*10), size=8, ha='center')
[[plot_fun(i,j) for i in range(10)] for j in range(10)]
# Set the range of the graph
ax.set_xlim(0, 10)
ax.set_ylim(0, 10)
plt.tick_params(axis='both',
which='both',
bottom='off',
top='off',
labelbottom='off',
right='off',
left='off',
labelleft='off',
)
# Draw it!
start_x, start_y = [1 - 0.5, 10 - 0.5]
plt.text(start_x, start_y - 0.25, 'START', ha='center')
plt.text(start_y, start_x - 0.25, 'GOAL', ha='center')
line, =ax.plot([start_x], [start_y], marker="o", color='g', markersize=35)
line, =ax.plot([start_y], [start_x], marker="o", color='y', markersize=35)
# Set the Strategy parameters theta_0 (The Strategy Table)
N = np.nan
# up, right, down, left
theta_0_row9 = np.array([
[ N, 1, 1, N],# S_0
[ N, 1, N, 1],# S_1
[ N, 1, 1, 1],# S_2
[ N, 1, 1, 1],# S_3
[ N, 1, 1, 1],# S_4
[ N, 1, 1, 1],# S_5
[ N, 1, 1, 1],# S_6
[ N, 1, 1, 1],# S_7
[ N, 1, 1, 1],# S_8
[ N, N, 1, 1],# S_9
])
theta_0_row8 = np.array([
[ 1, 1, 1, N],# S_10
[ N, N, 1, 1],# S_11
[ 1, 1, N, N],# S_12
[ 1, 1, N, 1],# S_13
[ 1, 1, N, 1],# S_14
[ 1, 1, N, 1],# S_15
[ 1, 1, N, 1],# S_16
[ 1, 1, N, 1],# S_17
[ 1, 1, N, 1],# S_18
[ 1, N, N, 1],# S_19
])
theta_0_row7 = np.array([
[ 1, N, 1, N],# S_20
[ 1, 1, N, N],# S_21
[ N, 1, N, 1],# S_22
[ N, 1, N, 1],# S_23
[ N, 1, N, 1],# S_24
[ N, 1, N, 1],# S_25
[ N, 1, N, 1],# S_26
[ N, 1, N, 1],# S_27
[ N, 1, N, 1],# S_28
[ N, N, 1, 1],# S_29
])
theta_0_row6 = np.array([
[ 1, N, 1, N],# S_30
[ N, 1, N, N],# S_31
[ N, 1, N, 1],# S_32
[ N, 1, 1, 1],# S_33
[ N, 1, N, 1],# S_34
[ N, 1, N, 1],# S_35
[ N, 1, N, 1],# S_36
[ N, 1, N, 1],# S_37
[ N, 1, N, 1],# S_38
[ 1, N, 1, 1],# S_39
])
theta_0_row5 = np.array([
[ 1, N, 1, N],# S_40
[ N, 1, 1, N],# S_41
[ N, N, 1, 1],# S_42
[ 1, 1, N, N],# S_43
[ N, N, 1, 1],# S_44
[ N, 1, 1, N],# S_45
[ N, N, 1, 1],# S_46
[ N, 1, 1, N],# S_47
[ N, N, 1, 1],# S_48
[ 1, N, 1, N],# S_49
])
theta_0_row4 = np.array([
[ 1, N, 1, N],# S_50
[ 1, N, 1, N],# S_51
[ 1, N, 1, N],# S_52
[ N, N, 1, N],# S_53
[ 1, N, 1, N],# S_54
[ 1, N, 1, N],# S_55
[ 1, N, 1, N],# S_56
[ 1, N, 1, N],# S_57
[ 1, N, 1, N],# S_58
[ 1, N, 1, N],# S_59
])
theta_0_row3 = np.array([
[ 1, N, 1, N],# S_60
[ 1, N, 1, N],# S_61
[ 1, N, 1, N],# S_62
[ 1, N, 1, N],# S_63
[ 1, N, 1, N],# S_64
[ 1, N, 1, N],# S_65
[ 1, N, 1, N],# S_66
[ 1, N, 1, N],# S_67
[ 1, N, 1, N],# S_68
[ 1, N, 1, N],# S_69
])
theta_0_row2 = np.array([
[ 1, N, 1, N],# S_70
[ 1, N, 1, N],# S_71
[ 1, N, 1, N],# S_72
[ 1, N, 1, N],# S_73
[ 1, N, 1, N],# S_74
[ 1, N, 1, N],# S_75
[ 1, N, 1, N],# S_76
[ 1, N, 1, N],# S_77
[ 1, N, 1, N],# S_78
[ 1, N, 1, N],# S_79
])
theta_0_row1 = np.array([
[ 1, N, 1, N],# S_80
[ 1, N, 1, N],# S_81
[ 1, N, 1, N],# S_82
[ 1, N, 1, N],# S_83
[ 1, N, 1, N],# S_84
[ 1, N, 1, N],# S_85
[ 1, N, 1, N],# S_86
[ 1, N, 1, N],# S_87
[ 1, N, 1, N],# S_88
[ 1, N, N, N],# S_89
])
theta_0_row0 = np.array([
[ 1, 1, N, N],# S_90
[ 1, N, N, 1],# S_91
[ 1, 1, N, N],# S_92
[ 1, N, N, 1],# S_93
[ 1, 1, N, N],# S_94
[ 1, N, N, 1],# S_95
[ 1, 1, N, N],# S_96
[ 1, N, N, 1],# S_97
[ 1, 1, N, N],# S_98
[ 1, N, N, 1],# S_99
])
theta_0 = np.concatenate([
theta_0_row9,
theta_0_row8,
theta_0_row7,
theta_0_row6,
theta_0_row5,
theta_0_row4,
theta_0_row3,
theta_0_row2,
theta_0_row1,
theta_0_row0,
])
#theta_0
def softmax_convert_into_pi_from_theta(theta):
# Using Softmax function to calculate the percentage
beta = 1.0
[m, n] = theta.shape
pi = np.zeros((m, n))
exp_theta = np.exp(beta * theta)
for i in range(0, m):
# The straight-forward way of calculating percentage
#pi[i, :] = theta[i, :] / np.nansum(theta[i, :])
# The softmax way of calculating percentage
pi[i, :] = exp_theta[i, :] / np.nansum(exp_theta[i, :])
pi = np.nan_to_num(pi)
return pi
#pi_0 = simple_convert_into_pi_from_theta(theta_0)
pi_0 = softmax_convert_into_pi_from_theta(theta_0)
#pi_0
# Get Next Stage
def get_action_and_next_s(pi, s):
direction = ["up", "right", "down", "left"]
# Choose the direction according to the probability of pi[s,:]
next_direction = np.random.choice(direction, p=pi[s,:])
if next_direction == "up":
action = 0
s_next = s - 10
elif next_direction == "right":
action = 1
s_next = s + 1
elif next_direction == "down":
action = 2
s_next = s + 10
elif next_direction == "left":
action = 3
s_next = s - 1
return [action, s_next]
def goal_maze_return_state_and_action(pi):
s = 0 # At the starting point
state_and_action_history = [[0, np.nan]]
while True:
[action, next_s] = get_action_and_next_s(pi, s)
state_and_action_history[-1][1] = action
state_and_action_history.append([next_s, np.nan])
if next_s == 99:
break
else:
s = next_s
return state_and_action_history
state_and_action_history = goal_maze_return_state_and_action(pi_0)
#print("The total steps used to finish the maze is " + str(len(state_and_action_history)-1))
state_and_action_history_cutted = state_and_action_history.copy()
#print(state_and_action_history_cutted)
# Define the Update function of theta parameter
def update_theta(theta, pi, s_a_history):
eta = 0.1 # learning rate defined
T = len(state_and_action_history) - 1
# the total number of steps to reach the goal
[m, n] = theta.shape
delta_theta = theta.copy()
# Calculate delta_theta for each elements
for i in range(0, m):
for j in range(0, n):
if not(np.isnan(theta[i, j])):
SA_i = [ SA for SA in state_and_action_history if SA[0] == i ]
SA_ij = [ SA for SA in state_and_action_history if SA == [i, j]]
N_i = len(SA_i)
N_ij = len(SA_ij)
delta_theta[i, j] = (N_ij - pi[i, j] * N_i) / T
new_theta = theta + eta * delta_theta
return new_theta
new_theta = update_theta(theta_0, pi_0, state_and_action_history)
pi = softmax_convert_into_pi_from_theta(new_theta)
#print(pi)
# 方策勾配法で迷路を解く
# 初版で、def update_thetaに間違いがあった関係で、終了条件を変更します（修正日：180703）
#stop_epsilon = 10**-8 # 10^-8よりも方策に変化が少なくなったら学習終了とする
stop_epsilon = 10**-4 # 10^-4よりも方策に変化が少なくなったら学習終了とする
theta = theta_0
pi = pi_0
is_continue = True
count = 1
while is_continue: # is_continueがFalseになるまで繰り返す
state_and_action_history = goal_maze_return_state_and_action(pi) # 方策πで迷路内を探索した履歴を求める
new_theta = update_theta(theta, pi, state_and_action_history) # パラメータΘを更新
new_pi = softmax_convert_into_pi_from_theta(new_theta) # 方策πの更新
print(np.sum(np.abs(new_pi - pi))) # 方策の変化を出力
print(str(count)+" : The total steps used to finish the maze is " + str(len(state_and_action_history) - 1))
count += 1
if np.sum(np.abs(new_pi - pi)) < stop_epsilon:
is_continue = False
else:
theta = new_theta
pi = new_pi
state_and_action_history_cutted = state_and_action_history.copy()
print(state_and_action_history_cutted)
# 最終的な方策を確認
np.set_printoptions(precision=3, suppress=True) # 有効桁数3、指数表示しないという設定
print(pi)
# エージェントの移動の様子を可視化します
# 参考URL http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/
'''
import matplotlib
from matplotlib import animation, rc
matplotlib.rcParams['animation.embed_limit'] = 2**128
'''
#from IPython.display import HTML
def init():
'''背景画像の初期化'''
line.set_data([], [])
return (line,)
def animate(i):
'''フレームごとの描画内容'''
state = state_and_action_history_cutted[i][0] # 現在の場所を描く
x = (state % 10) + 0.5 # 状態のx座標は、3で割った余り+0.5
y = 9.5 - int(state / 10) # y座標は3で割った商を9.5から引く
line.set_data(x, y)
return (line,)
# 初期化関数とフレームごとの描画関数を用いて動画を作成する
anim = animation.FuncAnimation(fig, animate, init_func=init, frames=len( state_and_action_history_cutted), interval=200, repeat=False)
#HTML(anim.to_jshtml())
#rc('animation', html='jshtml')
#anim
anim.save("maze_RL_Policy_Gradient.mp4")