蒙特卡洛树搜索（MCTS）代码详解【python】

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蒙特卡洛树搜索（MCTS）代码详解【python】

2023-08-26 00:31| 来源: 网络整理| 查看: 265

前文：

AlphaGo Zero 详解

后文：

AlphaZero五子棋网络模型【python】

之前看了AlphaGo Zero 的整个流程，接下来就要了解一下具体怎么实现的。毕设选择做用 AlphaGoZero 做五子棋，也在网上找到了相当不错的前人写的代码。我要做的是先看懂他写的，然后再试试改进算法的性能。

首先要实现 MCTS 的部分，原版注释用英语写的。现在我要一步一步的分析。

首先创建节点类 TreeNode：

class TreeNode(object): def __init__(self, parent, prior_p): self._parent = parent self._children = {} self._n_visits = 0 self._Q = 0 self._u = 0 self._P = prior_p def select(self, c_puct): def expand(self, action_priors): def update(self, leaf_value): def update_recursive(self, leaf_value): def get_value(self, c_puct): def is_leaf(self): def is_root(self):

TreeNode 类里初始化了一些数值，主要是父节点，子节点，访问节点的次数，Q值和u值，还有先验概率。他还定义了一些函数：

def select(self, c_puct): return max(self._children.items(), key=lambda act_node: act_node[1].get_value(c_puct)) def get_value(self, c_puct): self._u = c_puct * self._P * np.sqrt(self._parent._n_visits) / (1 + self._n_visits) return self._Q + self._u

select() 的功能：选择在子节中选择具有（Q+u）最大的节点，c_puct是需要我们定义的值，在后面会说到。

def expand(self, action_priors): for action, prob in action_priors: if action not in self._children: self._children[action] = TreeNode(self, prob)

expand() 的功能：扩展输入action_priors 是一个包括的所有合法动作的列表（list），表示在当前局面我可以在哪些地方落子。此函数为当前节点扩展了子节点。

def update(self, leaf_value): # Count visit. self._n_visits += 1 # Update Q, a running average of values for all visits. self._Q += 1.0*(leaf_value - self._Q) / self._n_visits def update_recursive(self, leaf_value): # If it is not root, this node's parent should be updated first. if self._parent: self._parent.update_recursive(-leaf_value) self.update(leaf_value)

update_recursive() 的功能：回溯从该节点开始，自上而下地更新所有的父节点。

另外还有两个函数

def is_leaf(self): return self._children == {} def is_root(self): return self._parent is None

用来判断当前节点是否是叶节点或根节点。

以上是MCTS中的三个流程（一二四），我们发现还少了一个最重要的第三步：模拟，模拟的步骤写在了 MCTS类中。

class MCTS(object): def __init__(self, policy_value_fn, c_puct=5, n_playout=10000): self._root = TreeNode(None, 1.0) self._policy = policy_value_fn self._c_puct = c_puct self._n_playout = n_playout def _playout(self, state): node = self._root while True: if node.is_leaf(): break # Greedily select next move. action, node = node.select(self._c_puct) state.do_move(action) # Evaluate the leaf using a network which outputs a list of (action, probability) # tuples p and also a score v in [-1, 1] for the current player. action_probs, leaf_value = self._policy(state) # Check for end of game. end, winner = state.game_end() if not end: node.expand(action_probs) else: # for end state，return the "true" leaf_value if winner == -1: # tie leaf_value = 0.0 else: leaf_value = 1.0 if winner == state.get_current_player() else -1.0 # Update value and visit count of nodes in this traversal. node.update_recursive(-leaf_value) def get_move_probs(self, state, temp=1e-3): for n in range(self._n_playout): state_copy = copy.deepcopy(state) self._playout(state_copy) act_visits = [(act, node._n_visits) for act, node in self._root._children.items()] acts, visits = zip(*act_visits) act_probs = softmax(1.0/temp * np.log(visits)) return acts, act_probs def update_with_move(self, last_move): if last_move in self._root._children: self._root = self._root._children[last_move] self._root._parent = None else: self._root = TreeNode(None, 1.0) def __str__(self): return "MCTS"

MCTS类的初始输入参数：

policy_value_fn：当前采用的策略函数，输入是当前棋盘的状态，输出 (action, prob)元祖和score[-1,1]。c_puct：控制探索和回报的比例，值越大表示越依赖之前的先验概率。n_playout：MCTS的执行次数，值越大，消耗的时间越多，效果也越好。

他还定义了一个根节点 self._root = TreeNode(None, 1.0) 父节点：None，先验概率：1.0

_playout(self, state)：此函数有一个输入参数：state, 它表示当前的状态。这个函数的功能就是模拟。它根据当前的状态进行游戏，用贪心算法一条路走到黑，直到叶子节点，再判断游戏结束与否。如果游戏没有结束，则扩展节点，否则回溯更新叶子节点和所有祖先的值。

get_move_probs(self, state, temp)：之前所有的代码都是为这个函数做铺垫。它的功能是从当前状态开始获得所有可行行动以及它们的概率。也就是说它能根据棋盘的状态，结合之前介绍的代码，告诉你它计算的结果，在棋盘的各个位置落子的胜率是多少。有了它，我们就能让计算机学会下棋。

update_with_move(self, last_move)：自我对弈时，每走一步之后更新MCTS的子树。与玩家对弈时，每一个回合都要重置子树。

接下来构建一个MCTS的玩家

class MCTSPlayer(object): """AI player based on MCTS""" def __init__(self, policy_value_function, c_puct=5, n_playout=2000, is_selfplay=0): self.mcts = MCTS(policy_value_function, c_puct, n_playout) self._is_selfplay = is_selfplay def set_player_ind(self, p): self.player = p def reset_player(self): self.mcts.update_with_move(-1) def get_action(self, board, temp=1e-3, return_prob=0): sensible_moves = board.availables move_probs = np.zeros(board.width * board.height) # the pi vector returned by MCTS as in the alphaGo Zero paper if len(sensible_moves) > 0: acts, probs = self.mcts.get_move_probs(board, temp) move_probs[list(acts)] = probs if self._is_selfplay: # add Dirichlet Noise for exploration (needed for self-play training) move = np.random.choice(acts, p=0.75 * probs + 0.25 * np.random.dirichlet(0.3 * np.ones(len(probs)))) self.mcts.update_with_move(move) # update the root node and reuse the search tree else: # with the default temp=1e-3, this is almost equivalent to choosing the move with the highest prob move = np.random.choice(acts, p=probs) # reset the root node self.mcts.update_with_move(-1) if return_prob: return move, move_probs else: return move else: print("WARNING: the board is full")

MCTSPlayer类的主要功能在函数get_action(self, board, temp=1e-3, return_prob=0)里实现。自我对弈的时候会有一定的探索几率，用来训练。与人类下棋是总是选择最优策略，用来检测训练成果。

完整代码：

import numpy as np import copy def softmax(x): probs = np.exp(x - np.max(x)) probs /= np.sum(probs) return probs class TreeNode(object): """A node in the MCTS tree. Each node keeps track of its own value Q, prior probability P, and its visit-count-adjusted prior score u. """ def __init__(self, parent, prior_p): self._parent = parent self._children = {} # a map from action to TreeNode self._n_visits = 0 self._Q = 0 self._u = 0 self._P = prior_p def expand(self, action_priors): """Expand tree by creating new children. action_priors -- output from policy function - a list of tuples of actions and their prior probability according to the policy function. """ for action, prob in action_priors: if action not in self._children: self._children[action] = TreeNode(self, prob) def select(self, c_puct): """Select action among children that gives maximum action value, Q plus bonus u(P). Returns: A tuple of (action, next_node) """ return max(self._children.items(), key=lambda act_node: act_node[1].get_value(c_puct)) def update(self, leaf_value): """Update node values from leaf evaluation. """ # Count visit. self._n_visits += 1 # Update Q, a running average of values for all visits. self._Q += 1.0*(leaf_value - self._Q) / self._n_visits def update_recursive(self, leaf_value): """Like a call to update(), but applied recursively for all ancestors. """ # If it is not root, this node's parent should be updated first. if self._parent: self._parent.update_recursive(-leaf_value) self.update(leaf_value) def get_value(self, c_puct): """Calculate and return the value for this node: a combination of leaf evaluations, Q, and this node's prior adjusted for its visit count, u c_puct -- a number in (0, inf) controlling the relative impact of values, Q, and prior probability, P, on this node's score. """ self._u = c_puct * self._P * np.sqrt(self._parent._n_visits) / (1 + self._n_visits) return self._Q + self._u def is_leaf(self): """Check if leaf node (i.e. no nodes below this have been expanded). """ return self._children == {} def is_root(self): return self._parent is None class MCTS(object): """A simple implementation of Monte Carlo Tree Search. """ def __init__(self, policy_value_fn, c_puct=5, n_playout=10000): """Arguments: policy_value_fn -- a function that takes in a board state and outputs a list of (action, probability) tuples and also a score in [-1, 1] (i.e. the expected value of the end game score from the current player's perspective) for the current player. c_puct -- a number in (0, inf) that controls how quickly exploration converges to the maximum-value policy, where a higher value means relying on the prior more """ self._root = TreeNode(None, 1.0) self._policy = policy_value_fn self._c_puct = c_puct self._n_playout = n_playout def _playout(self, state): """Run a single playout from the root to the leaf, getting a value at the leaf and propagating it back through its parents. State is modified in-place, so a copy must be provided. Arguments: state -- a copy of the state. """ node = self._root while True: if node.is_leaf(): break # Greedily select next move. action, node = node.select(self._c_puct) state.do_move(action) # Evaluate the leaf using a network which outputs a list of (action, probability) # tuples p and also a score v in [-1, 1] for the current player. action_probs, leaf_value = self._policy(state) # Check for end of game. end, winner = state.game_end() if not end: node.expand(action_probs) else: # for end state，return the "true" leaf_value if winner == -1: # tie leaf_value = 0.0 else: leaf_value = 1.0 if winner == state.get_current_player() else -1.0 # Update value and visit count of nodes in this traversal. node.update_recursive(-leaf_value) def get_move_probs(self, state, temp=1e-3): """Runs all playouts sequentially and returns the available actions and their corresponding probabilities Arguments: state -- the current state, including both game state and the current player. temp -- temperature parameter in (0, 1] that controls the level of exploration Returns: the available actions and the corresponding probabilities """ for n in range(self._n_playout): state_copy = copy.deepcopy(state) self._playout(state_copy) # calc the move probabilities based on the visit counts at the root node act_visits = [(act, node._n_visits) for act, node in self._root._children.items()] acts, visits = zip(*act_visits) act_probs = softmax(1.0/temp * np.log(visits)) return acts, act_probs def update_with_move(self, last_move): """Step forward in the tree, keeping everything we already know about the subtree. """ if last_move in self._root._children: self._root = self._root._children[last_move] self._root._parent = None else: self._root = TreeNode(None, 1.0) def __str__(self): return "MCTS" class MCTSPlayer(object): """AI player based on MCTS""" def __init__(self, policy_value_function, c_puct=5, n_playout=2000, is_selfplay=0): self.mcts = MCTS(policy_value_function, c_puct, n_playout) self._is_selfplay = is_selfplay def set_player_ind(self, p): self.player = p def reset_player(self): self.mcts.update_with_move(-1) def get_action(self, board, temp=1e-3, return_prob=0): sensible_moves = board.availables # the pi vector returned by MCTS as in the alphaGo Zero paper move_probs = np.zeros(board.width*board.height) if len(sensible_moves) > 0: acts, probs = self.mcts.get_move_probs(board, temp) move_probs[list(acts)] = probs if self._is_selfplay: # add Dirichlet Noise for exploration (needed for # self-play training) move = np.random.choice( acts, p=0.75*probs + 0.25*np.random.dirichlet(0.3*np.ones(len(probs))) ) # update the root node and reuse the search tree self.mcts.update_with_move(move) else: # with the default temp=1e-3, it is almost equivalent # to choosing the move with the highest prob move = np.random.choice(acts, p=probs) # reset the root node self.mcts.update_with_move(-1) # location = board.move_to_location(move) # print("AI move: %d,%d\n" % (location[0], location[1])) if return_prob: return move, move_probs else: return move else: print("WARNING: the board is full")

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蒙特卡洛树搜索（MCTS）代码详解【python】

蒙特卡洛树搜索（MCTS）代码详解【python】

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