问题描述
我已经研究 MCTS AI 好几天了。我尝试在 tic-tac-toe 上实现它，这是我能想到的最简单的游戏，但出于某种原因，我的 AI 不断做出错误的决定。我曾尝试更改 UCB1 探索常数的值、每次搜索的迭代次数，甚至是获胜、失败和平局所获得的分数（试图让平局更有价值，因为该 AI 仅排在第二位） ，并尝试获得平局，否则获胜）。截至目前，代码如下所示：
import random
import math
import copy
class tree:
def __init__(self,board):
self.board = board
self.visits = 0
self.score = 0
self.children = []
class mcts:
def search(self,mx,player,):
root = tree(mx)
for i in range(1200):
leaf = mcts.expand(self,root.board,root)
result = mcts.rollout(self,leaf)
mcts.backpropagate(self,leaf,root,result)
return mcts.best_child(self,root).board
def expand(self,root):
plays = mcts.generate_states(self,player) #all possible plays
if root.visits == 0:
for j in plays:
root.children.append(j) #create child_nodes in case they havent been created yet
for j in root.children:
if j.visits == 0:
return j #first iterations of the loop
for j in plays:
if mcts.final(self,j.board,player):
return j
return mcts.best_child(self,root) #choose the one with most potential
def rollout(self,leaf):
mx = leaf.board
aux = 1
while mcts.final(self,"O") != True:
if aux == 1: # "X" playing
possible_states = []
possible_nodes = mcts.generate_states(self,"X")
for i in possible_nodes:
possible_states.append(i.board)
if len(possible_states) == 1: mx = possible_states[0]
else:
choice = random.randrange(0,len(possible_states) - 1)
mx = possible_states[choice]
if mcts.final(self,"X"): #The play by "X" finished the game
break
elif aux == 0: # "O" playing
possible_states = []
possible_nodes = mcts.generate_states(self,"O")
for i in possible_nodes:
possible_states.append(i.board)
if len(possible_states) == 1: mx = possible_states[0]
else:
choice = random.randrange(0,len(possible_states) - 1)
mx = possible_states[choice]
aux += 1
aux = aux%2
if mcts.final(self,"X"):
for i in range(len(mx)):
for k in range(len(mx[i])):
if mx[i][k] == "-":
return -1 #loss
return 0 #tie
elif mcts.final(self,"O"):
for i in range(len(mx)):
for k in range(len(mx[i])):
if mx[i][k] == "-":
return 1 #win
def backpropagate(self,result): # updating our prospects stats
leaf.score += result
leaf.visits += 1
root.visits += 1
def generate_states(self,player):
possible_states = [] #generate child_nodes
for i in range(len(mx)):
for k in range(len(mx[i])):
if mx[i][k] == "-":
option = copy.deepcopy(mx)
option[i][k] = player
child_node = tree(option)
possible_states.append(child_node)
return possible_states
def final(self,player): #check if game is won
possible_draw = True
win = False
for i in mx: #lines
if i == [player,player]:
win = True
possible_draw = False
if mx[0][0] == player: #diagonals
if mx[1][1] == player:
if mx[2][2] == player:
win = True
possible_draw = False
if mx[0][2] == player:
if mx[1][1] == player:
if mx[2][0] == player:
win = True
possible_draw = False
for i in range(3): #columns
if mx[0][i] == player and mx[1][i] == player and mx[2][i] == player:
win = True
possible_draw = False
for i in range(3):
for k in range(3):
if mx[i][k] == "-":
possible_draw = False
if possible_draw:
return possible_draw
return win
def calculate_score(self,score,child_visits,parent_visits,c): #UCB1
return score / child_visits + c * math.sqrt(math.log(parent_visits) / child_visits)
def best_child(self,root): #returns most promising node
treshold = -1*10**6
for j in root.children:
potential = mcts.calculate_score(self,j.score,j.visits,root.visits,2)
if potential > treshold:
win_choice = j
treshold = potential
return win_choice
#todo the AI takes too long for each play,optimize that by finding the optimal approach in the rollout phase
首先，这个 AI 的目的是返回一个改变的矩阵，在这种情况下他可以做出最好的发挥。我发现自己在质疑 MCTS 算法是否是所有这些破坏游戏背后的原因，因为其实现中可能存在一些错误。话虽如此，在我看来，代码执行以下操作：
为什么它不起作用？为什么选择糟糕的游戏而不是最佳的游戏？是算法错误实现了吗？
解决方法
我的错误是在扩展阶段选择了访问次数最多的节点，而根据 UCB1 公式，它本应是最具潜力的节点。在实现一些 if 子句时，我也犯了一些错误，因为没有计算所有的损失。