通过简单的强化学习实现井字棋（Tic-Tac-Toe）
一、强化学习简介
强化学习的过程可以理解为Agent与Environment的交互、学习、进步的过程，在井字棋中，可以简单的将其中的一方理解为Agent，另一方为Environment。交互的过程中主要有一下4个要素：
状态（state）：指可能出现的情况或局面，在井字棋中指局面上的落子情况与先后手。
操作（action）：指从一个状态（state）到另一个状态（state）的过程，在井字棋中指下一步的落子。
价值（value）：衡量每一个状态（state）的好坏程度，在井字棋中指在当前局面下取胜的可能性。价值与状态的对应关系又称价值函数（value function）
增益（reward）：指每一个操作所带来的价值（value）的变化，在井字棋中指这一步下的好不好。
强化学习实际是在模拟人类学习的过程。设想一个小孩在学习井字棋，一开始他完全不会下，只知道胜利局面的value是最高的，失败局面的value是最低的，只能随便下一个位置（explore），这样随便下几局之后，他会学习到，将要导致胜利的前几步的value是比较高的，将要导致失败的前几步的value是比较低的，这时通过explore使他对每个状态value的有了新的认识。当然他也会利用现有的知识（exploit），每当落子前，他会考虑落子后棋盘上可能的所有局面（state），然后选择一个对自己最有利的（max value）位置下棋。通过exploit，他可以利用他自己的知识使自己获胜的概率达到最大。
二、井字棋的算法
1、训练
强化学习井字棋训练的过程如下：
重复epochs次
while true:
if 分出胜负或平局
返回结果，break
随机的选择explore或exploit
if 选择explore
随机的选择落点下棋
else 选择exploit
从value_table中查找对应最大value状态的落点下棋
根据新状态的value在value_table中更新原状态的value
其中“根据新状态的value在value_table中更新原状态的value” 是非常重要的一部分，决定了强化学习的学习方法，即能不能学到知识。由于井字棋状态逻辑非常简单，因此使用如下简单的表达式即可：
V(S)=V(S)+α(V(S′)−V(S))
V(S)=V(S)+α(V(S′)−V(S))
其中VV表示value function，SS表示当前状态，S′S′表示新状态，V(S)V(S)表示S的value，αα 表示学习率，是可以调整的超参。
另外还需要控制的参数有训练次数epochs和选择explore的概率ϵϵ 。
# -*- coding: utf-8 -*-
"""
Created on Tue Jun 11 13:51:32 2019
@author: judy.yuan
"""
import numpy as np
import pickle
BOARD_ROWS = 3
BOARD_COLS = 3
BOARD_SIZE = BOARD_ROWS * BOARD_COLS
class State:
def __init__(self):
# the board is represented by an n * n array,
# 1 represents a chessman of the player who moves first,
# -1 represents a chessman of another player
# 0 represents an empty position
self.data = np.zeros((BOARD_ROWS, BOARD_COLS))
self.winner = None
self.hash_val = None
self.end = None
# compute the hash value for one state, it's unique
def hash(self):
if self.hash_val is None:
self.hash_val = 0
for i in np.nditer(self.data):
self.hash_val = self.hash_val * 3 + i + 1
return self.hash_val
# check whether a player has won the game, or it's a tie
def is_end(self):
if self.end is not None:
return self.end
results = []
# check row
for i in range(BOARD_ROWS):
results.append(np.sum(self.data[i, :]))
# check columns
for i in range(BOARD_COLS):
results.append(np.sum(self.data[:, i]))
# check diagonals
trace = 0
reverse_trace = 0
for i in range(BOARD_ROWS):
trace += self.data[i, i]
reverse_trace += self.data[i, BOARD_ROWS - 1 - i]
results.append(trace)
results.append(reverse_trace)
for result in results:
if result == 3:
self.winner = 1
self.end = True
return self.end
if result == -3:
self.winner = -1
self.end = True
return self.end
# whether it's a tie
sum_values = np.sum(np.abs(self.data))
if sum_values == BOARD_SIZE:
self.winner = 0
self.end = True
return self.end
# game is still going on
self.end = False
return self.end
# @symbol: 1 or -1
# put chessman symbol in position (i, j)
def next_state(self, i, j, symbol):
new_state = State()
new_state.data = np.copy(self.data)
new_state.data[i, j] = symbol
return new_state
# print the board
def print_state(self):
for i in range(BOARD_ROWS):
print('-------------')
out = '| '
for j in range(BOARD_COLS):
if self.data[i, j] == 1:
token = '*'
elif self.data[i, j] == -1:
token = 'x'
else:
token = '0'
out += token + ' | '
print(out)
print('-------------')
def get_all_states_impl(current_state, current_symbol, all_states):
for i in range(BOARD_ROWS):
for j in range(BOARD_COLS):
if current_state.data[i][j] == 0:
new_state = current_state.next_state(i, j, current_symbol)
new_hash = new_state.hash()
if new_hash not in all_states:
is_end = new_state.is_end()
all_states[new_hash] = (new_state, is_end)
if not is_end:
get_all_states_impl(new_state, -current_symbol, all_states)
def get_all_states():
current_symbol = 1
current_state = State()
all_states = dict()
all_states[current_state.hash()] = (current_state, current_state.is_end())
get_all_states_impl(current_state, current_symbol, all_states)
return all_states
# all possible board configurations
all_states = get_all_states()
class Judger:
# @player1: the player who will move first, its chessman will be 1
# @player2: another player with a chessman -1
def __init__(self, player1, player2):
self.p1 = player1
self.p2 = player2
self.current_player = None
self.p1_symbol = 1
self.p2_symbol = -1
self.p1.set_symbol(self.p1_symbol)
self.p2.set_symbol(self.p2_symbol)
self.current_state = State()
def reset(self):
self.p1.reset()
self.p2.reset()
def alternate(self):
while True:
yield self.p1
yield self.p2
# @print_state: if True, print each board during the game
def play(self, print_state=False):
alternator = self.alternate()
self.reset()
current_state = State()
self.p1.set_state(current_state)
self.p2.set_state(current_state)
if print_state:
current_state.print_state()
while True:
player = next(alternator)
i, j, symbol = player.act()
next_state_hash = current_state.next_state(i, j, symbol).hash()
current_state, is_end = all_states[next_state_hash]
self.p1.set_state(current_state)
self.p2.set_state(current_state)
if print_state:
current_state.print_state()
if is_end:
return current_state.winner
# AI player
class Player:
# @step_size: the step size to update estimations
# @epsilon: the probability to explore
def __init__(self, step_size=0.1, epsilon=0.1):
self.estimations = dict()
self.step_size = step_size
self.epsilon = epsilon
self.states = []
self.greedy = []
self.symbol = 0
def reset(self):
self.states = []
self.greedy = []
def set_state(self, state):
self.states.append(state)
self.greedy.append(True)
def set_symbol(self, symbol):
self.symbol = symbol
for hash_val in all_states:
state, is_end = all_states[hash_val]
if is_end:
if state.winner == self.symbol:
self.estimations[hash_val] = 1.0
elif state.winner == 0:
# we need to distinguish between a tie and a lose
self.estimations[hash_val] = 0.5
else:
self.estimations[hash_val] = 0
else:
self.estimations[hash_val] = 0.5
# update value estimation
def backup(self):
states = [state.hash() for state in self.states]
for i in reversed(range(len(states) - 1)):
state = states[i]
td_error = self.greedy[i] * (
self.estimations[states[i + 1]] - self.estimations[state]
)
self.estimations[state] += self.step_size * td_error
# choose an action based on the state
def act(self):
state = self.states[-1]
next_states = []
next_positions = []
for i in range(BOARD_ROWS):
for j in range(BOARD_COLS):
if state.data[i, j] == 0:
next_positions.append([i, j])
next_states.append(state.next_state(
i, j, self.symbol).hash())
if np.random.rand() < self.epsilon:
action = next_positions[np.random.randint(len(next_positions))]
action.append(self.symbol)
self.greedy[-1] = False
return action
values = []
for hash_val, pos in zip(next_states, next_positions):
values.append((self.estimations[hash_val], pos))
# to select one of the actions of equal value at random due to Python's sort is stable
np.random.shuffle(values)
values.sort(key=lambda x: x[0], reverse=True)
action = values[0][1]
action.append(self.symbol)
return action
def save_policy(self):
with open('policy_%s.bin' % ('first' if self.symbol == 1 else 'second'), 'wb') as f:
pickle.dump(self.estimations, f)
def load_policy(self):
with open('policy_%s.bin' % ('first' if self.symbol == 1 else 'second'), 'rb') as f:
self.estimations = pickle.load(f)
# human interface
# input a number to put a chessman
# | q | w | e |
# | a | s | d |
# | z | x | c |
class HumanPlayer:
def __init__(self, **kwargs):
self.symbol = None
self.keys = ['q', 'w', 'e', 'a', 's', 'd', 'z', 'x', 'c']
self.state = None
def reset(self):
pass
def set_state(self, state):
self.state = state
def set_symbol(self, symbol):
self.symbol = symbol
def act(self):
self.state.print_state()
key = input("Input your position:")
data = self.keys.index(key)
i = data // BOARD_COLS
j = data % BOARD_COLS
return i, j, self.symbol
def train(epochs, print_every_n=500):
player1 = Player(epsilon=0.01)
player2 = Player(epsilon=0.01)
judger = Judger(player1, player2)
player1_win = 0.0
player2_win = 0.0
for i in range(1, epochs + 1):
winner = judger.play(print_state=False)
if winner == 1:
player1_win += 1
if winner == -1:
player2_win += 1
if i % print_every_n == 0:
print('Epoch %d, player 1 winrate: %.02f, player 2 winrate: %.02f' % (i, player1_win / i, player2_win / i))
player1.backup()
player2.backup()
judger.reset()
player1.save_policy()
player2.save_policy()
def compete(turns):
player1 = Player(epsilon=0)
player2 = Player(epsilon=0)
judger = Judger(player1, player2)
player1.load_policy()
player2.load_policy()
player1_win = 0.0
player2_win = 0.0
for _ in range(turns):
winner = judger.play()
if winner == 1:
player1_win += 1
if winner == -1:
player2_win += 1
judger.reset()
print('%d turns, player 1 win %.02f, player 2 win %.02f' % (turns, player1_win / turns, player2_win / turns))
# The game is a zero sum game. If both players are playing with an optimal strategy, every game will end in a tie.
# So we test whether the AI can guarantee at least a tie if it goes second.
def play():
while True:
player1 = HumanPlayer()
player2 = Player(epsilon=0)
judger = Judger(player1, player2)
player2.load_policy()
winner = judger.play()
if winner == player2.symbol:
print("You lose!")
elif winner == player1.symbol:
print("You win!")
else:
print("It is a tie!")
if __name__ == '__main__':
train(int(1e5))
compete(int(1e3))
play()