Я потратил некоторое время, чтобы прочитать о MCTS, и еще больше времени, чтобы поймать остальные ошибки:
- Я добавил OXOState (tic-tac-toe), чтобы я мог отлаживать с помощью знакомых ипростая играЭто была только одна проблема с исходным исходным кодом http://mcts.ai/code/python.html:, он продолжит играть после того, как кто-то выиграет игру.Итак, я исправил это.
- Для отладки и веселья добавлен HumanPlayer.
- Для оценки уровня игры добавлены RandomPlayer и NegamaxPlayer (алгоритм negamax https://en.wikipedia.org/wiki/Negamax)
NegamaxPlayer против UCT (поиск по дереву Монте-Карло)
itermax= won lost draw total_time
1 964 0 36 172.8
10 923 0 77 173.4
100 577 0 423 182.1
1000 48 0 952 328.9
10000 0 0 1000 1950.3
UTC играет весьма впечатляюще против идеального игрока (минимакс выполняет три поиска): при itermax = 1000 счет и время для игры почти равны- только 48 проигранных игр из 1000.
Исправлены остальные (я думаю) проблемы с BigGameState.Теперь он играет очень умело, поэтому я не могу выиграть.
Я добавил ограничение глубины в NegamaxPlayer, чтобы играть в крестики-нолики на 9 досках, поскольку поиск лучшего хода в этой игре может занять некоторое время.,
NegamaxPlayer (глубина) против UCT (itermax)
depth itermax won lost draw total_time
4 1 9 1 0 18.4
4 10 9 1 0 20.7
4 100 5 5 0 36.2
4 1000 2 8 0 188.8
5 10000 2 8 0 318.0
6 10000 0 10 0 996.5
Теперь UTC (itermax = 100) воспроизводит тот же уровень, что и NegamaxPlayer (глубина 4), и побеждает на следующем уровне 8-2.Я поражен!; -)
Я выиграл первую игру, в которую когда-либо играл на уровне (itermax = 100), но проиграл вторую игру на уровне 1000:
Game 1, Move 40:
┏━━━━━━━┳━━━━━━━┳━━━━━━━┓
┃ X X . ┃*O O O ┃ O . . ┃
┃ . O O ┃ . . X ┃ . X O ┃
┃ O X X ┃ X . . ┃ . X . ┃
┣━━━━━━━╋━━━━━━━╋━━━━━━━┫
┃ X . . ┃ . X . ┃ O . . ┃
┃ . X . ┃ O O X ┃ O X . ┃
┃ . O . ┃ O . . ┃ X . . ┃
┣━━━━━━━╋━━━━━━━╋━━━━━━━┫
┃ X X O ┃ O . X ┃ . O X ┃
┃ X . . ┃ . . . ┃ . . . ┃
┃ . . O ┃ O . X ┃ . O . ┃
┗━━━━━━━┻━━━━━━━┻━━━━━━━┛
Player 2 wins!
won 0 lost 1 draw 0
Вот полный код:
from math import *
import random
import time
from copy import deepcopy
class BigGameState:
def __init__(self):
self.board = [[0 for i in range(10)] for j in range(10)]
self.curr = 1
# At the root pretend the player just moved is player 2,
# so player 1 will have the first move
self.playerJustMoved = 2
self.ended = False
# to put * in __str__
self.last_move = None
self.last_curr = None
def Clone(self):
return deepcopy(self)
def DoMove(self, move):
# 1 2 3
# 4 5 6
# 7 8 9
winning_pairs = [[], # 0
[[2, 3], [5, 9], [4, 7]], # for 1
[[1, 3], [5, 8]], # for 2
[[1, 2], [5, 7], [6, 9]], # for 3
[[1, 7], [5, 6]], # for 4
[[1, 9], [2, 8], [3, 7], [4, 6]], # for 5
[[3, 9], [4, 5]], # for 6
[[1, 4], [5, 3], [8, 9]], # for 7
[[7, 9], [2, 5]], # for 8
[[7, 8], [1, 5], [3, 6]], # for 9
]
if not isinstance(move, int) or 1 < move > 9 or \
self.board[self.curr][move] != 0:
raise ValueError
self.playerJustMoved = 3 - self.playerJustMoved
self.board[self.curr][move] = self.playerJustMoved
for index1, index2 in winning_pairs[move]:
if self.playerJustMoved == self.board[self.curr][index1] == \
self.board[self.curr][index2]:
self.ended = True
self.last_move = move
self.last_curr = self.curr
self.curr = move
def GetMoves(self):
if self.ended:
return []
return [i for i in range(1, 10) if self.board[self.curr][i] == 0]
def GetResult(self, playerjm):
# Get the game result from the viewpoint of playerjm.
for bo in self.board:
for x, y, z in [(1, 2, 3), (4, 5, 6), (7, 8, 9),
(1, 4, 7), (2, 5, 8), (3, 6, 9),
(1, 5, 9), (3, 5, 7)]:
if bo[x] == bo[y] == bo[z]:
if bo[x] == playerjm:
return 1.0
elif bo[x] != 0:
return 0.0
if not self.GetMoves():
return 0.5 # draw
raise ValueError
def _one_board_string(self, a, row):
return ''.join([' ' + '.XO'[self.board[a][i+row]] for i in range(3)])
def _three_board_line(self, index, row):
return '┃' + ''.join([self._one_board_string(i + index, row) + ' ┃' for i in range(3)])
def __repr__(self):
# ┏━━━━━━━┳━━━━━━━┳━━━━━━━┓
# ┃ . . . ┃ . . . ┃ . . . ┃
# ┃ . . . ┃ X . X ┃ . . O ┃
# ┃ . X . ┃ . . O ┃ . . . ┃
# ┣━━━━━━━╋━━━━━━━╋━━━━━━━┫
# ┃ . . . ┃ . . . ┃*X X X ┃
# ┃ X . O ┃ . . . ┃ O . O ┃
# ┃ . . O ┃ . . . ┃ . . . ┃
# ┣━━━━━━━╋━━━━━━━╋━━━━━━━┫
# ┃ . . . ┃ . O . ┃ . O . ┃
# ┃ . . . ┃ . . . ┃ . . X ┃
# ┃ . . . ┃ . . . ┃ . . X ┃
# ┗━━━━━━━┻━━━━━━━┻━━━━━━━┛
s = '┏━━━━━━━┳━━━━━━━┳━━━━━━━┓\n'
for i in [1, 4, 7]:
for j in [1, 4, 7]:
s += self._three_board_line(i, j) + '\n'
if i != 7:
s += '┣━━━━━━━╋━━━━━━━╋━━━━━━━┫\n'
else:
s += '┗━━━━━━━┻━━━━━━━┻━━━━━━━┛\n'
# Hack: by rows and colums of move and current board
# calculate place to put '*' so it is visible
c = self.last_curr - 1
c_c = c % 3
c_r = c // 3
m_c = (self.last_move - 1) % 3
m_r = (self.last_move - 1)// 3
p = 26 + c_r * (26 * 4) + c_c * 8 + m_r * 26 + m_c * 2 + 1
s = s[:p] + '*' + s[p+1:]
return s
class OXOState:
def __init__(self):
self.playerJustMoved = 2
self.ended = False
self.board = [0, 0, 0, 0, 0, 0, 0, 0, 0]
def Clone(self):
return deepcopy(self)
def DoMove(self, move):
# 0 1 2
# 3 4 5
# 6 7 8
winning_pairs = [[[1, 2], [4, 8], [3, 6]], # for 0
[[0, 2], [4, 7]], # for 1
[[0, 1], [4, 6], [5, 8]], # for 2
[[0, 6], [4, 5]], # for 3
[[0, 8], [1, 7], [2, 6], [3, 5]], # for 4
[[2, 8], [3, 4]], # for 5
[[0, 3], [4, 2], [7, 8]], # for 6
[[6, 8], [1, 4]], # for 7
[[6, 7], [0, 4], [2, 5]], # for 6
]
if not isinstance(move, int) or 0 < move > 8 or \
self.board[move] != 0:
raise ValueError
self.playerJustMoved = 3 - self.playerJustMoved
self.board[move] = self.playerJustMoved
for index1, index2 in winning_pairs[move]:
if self.playerJustMoved == self.board[index1] == self.board[index2]:
self.ended = True
def GetMoves(self):
return [] if self.ended else [i for i in range(9) if self.board[i] == 0]
def GetResult(self, playerjm):
for (x, y, z) in [(0, 1, 2), (3, 4, 5), (6, 7, 8), (0, 3, 6), (1, 4, 7),
(2, 5, 8), (0, 4, 8), (2, 4, 6)]:
if self.board[x] == self.board[y] == self.board[z]:
if self.board[x] == playerjm:
return 1.0
elif self.board[x] != 0:
return 0.0
if self.GetMoves() == []:
return 0.5 # draw
raise ValueError
def __repr__(self):
s = ""
for i in range(9):
s += '.XO'[self.board[i]]
if i % 3 == 2: s += "\n"
return s
class Node:
""" A node in the game tree. Note wins is always from the viewpoint of playerJustMoved.
Crashes if state not specified.
"""
def __init__(self, move=None, parent=None, state=None):
self.move = move # the move that got us to this node - "None" for the root node
self.parentNode = parent # "None" for the root node
self.childNodes = []
self.wins = 0
self.visits = 0
self.untriedMoves = state.GetMoves() # future child nodes
self.playerJustMoved = state.playerJustMoved # the only part of the state that the Node needs later
def UCTSelectChild(self):
""" Use the UCB1 formula to select a child node. Often a constant UCTK is applied so we have
lambda c: c.wins/c.visits + UCTK * sqrt(2*log(self.visits)/c.visits to vary the amount of
exploration versus exploitation.
"""
s = sorted(self.childNodes, key=lambda c: c.wins / c.visits + sqrt(
2 * log(self.visits) / c.visits))[-1]
return s
def AddChild(self, m, s):
""" Remove m from untriedMoves and add a new child node for this move.
Return the added child node
"""
n = Node(move=m, parent=self, state=s)
self.untriedMoves.remove(m)
self.childNodes.append(n)
return n
def Update(self, result):
""" Update this node - one additional visit and result additional wins. result must be from the viewpoint of playerJustmoved.
"""
self.visits += 1
self.wins += result
def __repr__(self):
return "[M:" + str(self.move) + " W/V:" + str(self.wins) + "/" + str(
self.visits) + " U:" + str(self.untriedMoves) + "]"
def TreeToString(self, indent):
s = self.IndentString(indent) + str(self)
for c in self.childNodes:
s += c.TreeToString(indent + 1)
return s
def IndentString(self, indent):
s = "\n"
for i in range(1, indent + 1):
s += "| "
return s
def ChildrenToString(self):
s = ""
for c in self.childNodes:
s += str(c) + "\n"
return s
def UCT(rootstate, itermax, verbose=False):
""" Conduct a UCT search for itermax iterations starting from rootstate.
Return the best move from the rootstate.
Assumes 2 alternating players (player 1 starts), with game results in the range [0.0, 1.0]."""
rootnode = Node(state=rootstate)
for i in range(itermax):
node = rootnode
state = rootstate.Clone()
# Select
while node.untriedMoves == [] and node.childNodes != []: # node is fully expanded and non-terminal
node = node.UCTSelectChild()
state.DoMove(node.move)
# Expand
if node.untriedMoves != []: # if we can expand (i.e. state/node is non-terminal)
m = random.choice(node.untriedMoves)
state.DoMove(m)
node = node.AddChild(m, state) # add child and descend tree
# Rollout - this can often be made orders of magnitude quicker using a state.GetRandomMove() function
while state.GetMoves() != []: # while state is non-terminal
state.DoMove(random.choice(state.GetMoves()))
# Backpropagate
while node != None: # backpropagate from the expanded node and work back to the root node
node.Update(state.GetResult(
node.playerJustMoved)) # state is terminal. Update node with result from POV of node.playerJustMoved
node = node.parentNode
# Output some information about the tree - can be omitted
# if (verbose):
# print(rootnode.TreeToString(0))
# else:
# print(rootnode.ChildrenToString())
return sorted(rootnode.childNodes, key=lambda c: c.visits)[
-1].move # return the move that was most visited
def HumanPlayer(state):
moves = state.GetMoves()
while True:
try:
m = int(input("Your move " + str(moves) + " : "))
if m in moves:
return m
except ValueError:
pass
def RandomPlayer(state):
return random.choice(state.GetMoves())
def negamax(board, color, depth): # ##################################################
moves = board.GetMoves()
if not moves:
x = board.GetResult(board.playerJustMoved)
if x == 0.0:
print('negamax ERROR:')
print(board)
print(board.playerJustMoved)
print(board.curr, board.ended)
print(board.GetMoves())
raise ValueError
if x == 0.5:
return 0.0, None
if color == 1 and board.playerJustMoved == 1:
return 1.0, None
else:
return -1.0, None
if depth == 0:
return 0.0, None
v = float("-inf")
best_move = []
for m in moves:
new_board = board.Clone()
new_board.DoMove(m)
x, _ = negamax(new_board, -color, depth - 1)
x = - x
if x >= v:
if x > v:
best_move = []
v = x
best_move.append(m)
if depth >=8:
print(depth, v, best_move)
return v, best_move
def NegamaxPlayer(game):
best_moves = game.GetMoves()
if len(best_moves) != 9:
_, best_moves = negamax(game, 1, 4)
print(best_moves)
return random.choice(best_moves)
if __name__ == "__main__":
def main():
random.seed(123456789)
won = 0
lost = 0
draw = 0
for i in range(10):
# state = OXOState() # uncomment to play OXO
state = BigGameState()
move = 0
while (state.GetMoves() != []):
if state.playerJustMoved == 1:
# m = RandomPlayer(state)
m = UCT(rootstate=state, itermax=100, verbose=False)
else:
# m = UCT(rootstate=state, itermax=100, verbose=False)
# m = NegamaxPlayer(state)
m = HumanPlayer(state)
# m = RandomPlayer(state)
state.DoMove(m)
move += 1
print('Game ', i + 1, ', Move ', move, ':\n', state, sep='')
if state.GetResult(1) == 1.0:
won += 1
print("Player 1 wins!")
elif state.GetResult(1) == 0.0:
lost += 1
print("Player 2 wins!")
else:
draw += 1
print("Nobody wins!")
print('won', won, 'lost', lost, 'draw', draw)
start_time = time.perf_counter()
main()
total_time = time.perf_counter() - start_time
print('total_time', total_time)