# Copyright 2018 The TensorFlow Authors. All Rights Reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================== """Monte Carlo Tree Search implementation. All terminology here (Q, U, N, p_UCT) uses the same notation as in the AlphaGo (AG) paper, and more details can be found in the paper. Here is a brief description: Q: the action value of a position U: the search control strategy N: the visit counts of a state p_UCT: the PUCT algorithm for action selection """ from __future__ import absolute_import from __future__ import division from __future__ import print_function import collections import math import coords import numpy as np # Exploration constant c_PUCT = 1.38 # Dirichlet noise, as a function of board_size def D_NOISE_ALPHA(board_size): return 0.03 * 361 / (board_size ** 2) class DummyNode(object): """A fake node of a MCTS search tree. This node is intended to be a placeholder for the root node, which would otherwise have no parent node. If all nodes have parents, code becomes simpler.""" def __init__(self, board_size): self.board_size = board_size self.parent = None self.child_N = collections.defaultdict(float) self.child_W = collections.defaultdict(float) class MCTSNode(object): """A node of a MCTS search tree. A node knows how to compute the action scores of all of its children, so that a decision can be made about which move to explore next. Upon selecting a move, the children dictionary is updated with a new node. position: A go.Position instance fmove: A move (coordinate) that led to this position, a a flattened coord (raw number between 0-N^2, with None a pass) parent: A parent MCTSNode. """ def __init__(self, board_size, position, fmove=None, parent=None): if parent is None: parent = DummyNode(board_size) self.board_size = board_size self.parent = parent self.fmove = fmove # move that led to this position, as flattened coords self.position = position self.is_expanded = False self.losses_applied = 0 # number of virtual losses on this node # using child_() allows vectorized computation of action score. self.illegal_moves = 1000 * (1 - self.position.all_legal_moves()) self.child_N = np.zeros([board_size * board_size + 1], dtype=np.float32) self.child_W = np.zeros([board_size * board_size + 1], dtype=np.float32) # save a copy of the original prior before it gets mutated by d-noise. self.original_prior = np.zeros([board_size * board_size + 1], dtype=np.float32) self.child_prior = np.zeros([board_size * board_size + 1], dtype=np.float32) self.children = {} # map of flattened moves to resulting MCTSNode def __repr__(self): return "" % ( self.position.recent[-1:], self.N, self.position.to_play) @property def child_action_score(self): return (self.child_Q * self.position.to_play + self.child_U - self.illegal_moves) @property def child_Q(self): return self.child_W / (1 + self.child_N) @property def child_U(self): return (c_PUCT * math.sqrt(1 + self.N) * self.child_prior / (1 + self.child_N)) @property def Q(self): return self.W / (1 + self.N) @property def N(self): return self.parent.child_N[self.fmove] @N.setter def N(self, value): self.parent.child_N[self.fmove] = value @property def W(self): return self.parent.child_W[self.fmove] @W.setter def W(self, value): self.parent.child_W[self.fmove] = value @property def Q_perspective(self): "Return value of position, from perspective of player to play." return self.Q * self.position.to_play def select_leaf(self): current = self pass_move = self.board_size * self.board_size while True: current.N += 1 # if a node has never been evaluated, we have no basis to select a child. if not current.is_expanded: break # HACK: if last move was a pass, always investigate double-pass first # to avoid situations where we auto-lose by passing too early. if (current.position.recent and current.position.recent[-1].move is None and current.child_N[pass_move] == 0): current = current.maybe_add_child(pass_move) continue best_move = np.argmax(current.child_action_score) current = current.maybe_add_child(best_move) return current def maybe_add_child(self, fcoord): """Add child node for fcoord if it doesn't already exist, and returns it.""" if fcoord not in self.children: new_position = self.position.play_move( coords.from_flat(self.board_size, fcoord)) self.children[fcoord] = MCTSNode( self.board_size, new_position, fmove=fcoord, parent=self) return self.children[fcoord] def add_virtual_loss(self, up_to): """Propagate a virtual loss up to the root node. Args: up_to: The node to propagate until. (Keep track of this! You'll need it to reverse the virtual loss later.) """ self.losses_applied += 1 # This is a "win" for the current node; hence a loss for its parent node # who will be deciding whether to investigate this node again. loss = self.position.to_play self.W += loss if self.parent is None or self is up_to: return self.parent.add_virtual_loss(up_to) def revert_virtual_loss(self, up_to): self.losses_applied -= 1 revert = -1 * self.position.to_play self.W += revert if self.parent is None or self is up_to: return self.parent.revert_virtual_loss(up_to) def revert_visits(self, up_to): """Revert visit increments. Sometimes, repeated calls to select_leaf return the same node. This is rare and we're okay with the wasted computation to evaluate the position multiple times by the dual_net. But select_leaf has the side effect of incrementing visit counts. Since we want the value to only count once for the repeatedly selected node, we also have to revert the incremented visit counts. """ self.N -= 1 if self.parent is None or self is up_to: return self.parent.revert_visits(up_to) def incorporate_results(self, move_probabilities, value, up_to): assert move_probabilities.shape == (self.board_size * self.board_size + 1,) # A finished game should not be going through this code path - should # directly call backup_value() on the result of the game. assert not self.position.is_game_over() if self.is_expanded: self.revert_visits(up_to=up_to) return self.is_expanded = True self.original_prior = self.child_prior = move_probabilities # initialize child Q as current node's value, to prevent dynamics where # if B is winning, then B will only ever explore 1 move, because the Q # estimation will be so much larger than the 0 of the other moves. # # Conversely, if W is winning, then B will explore all 362 moves before # continuing to explore the most favorable move. This is a waste of search. # # The value seeded here acts as a prior, and gets averaged into # Q calculations. self.child_W = np.ones([self.board_size * self.board_size + 1], dtype=np.float32) * value self.backup_value(value, up_to=up_to) def backup_value(self, value, up_to): """Propagates a value estimation up to the root node. Args: value: the value to be propagated (1 = black wins, -1 = white wins) up_to: the node to propagate until. """ self.W += value if self.parent is None or self is up_to: return self.parent.backup_value(value, up_to) def is_done(self): '''True if the last two moves were Pass or if the position is at a move greater than the max depth. ''' max_depth = (self.board_size ** 2) * 1.4 # 505 moves for 19x19, 113 for 9x9 return self.position.is_game_over() or self.position.n >= max_depth def inject_noise(self): dirch = np.random.dirichlet([D_NOISE_ALPHA(self.board_size)] * ( (self.board_size * self.board_size) + 1)) self.child_prior = self.child_prior * 0.75 + dirch * 0.25 def children_as_pi(self, squash=False): """Returns the child visit counts as a probability distribution, pi If squash is true, exponentiate the probabilities by a temperature slightly larger than unity to encourage diversity in early play and hopefully to move away from 3-3s """ probs = self.child_N if squash: probs = probs ** .95 return probs / np.sum(probs) def most_visited_path(self): node = self output = [] while node.children: next_kid = np.argmax(node.child_N) node = node.children.get(next_kid) if node is None: output.append("GAME END") break output.append("%s (%d) ==> " % ( coords.to_kgs(self.board_size, coords.from_flat(self.board_size, node.fmove)), node.N)) output.append("Q: {:.5f}\n".format(node.Q)) return ''.join(output) def mvp_gg(self): """ Returns most visited path in go-gui VAR format e.g. 'b r3 w c17...""" node = self output = [] while node.children and max(node.child_N) > 1: next_kid = np.argmax(node.child_N) node = node.children[next_kid] output.append("%s" % coords.to_kgs( self.board_size, coords.from_flat(self.board_size, node.fmove))) return ' '.join(output) def describe(self): sort_order = list(range(self.board_size * self.board_size + 1)) sort_order.sort(key=lambda i: ( self.child_N[i], self.child_action_score[i]), reverse=True) soft_n = self.child_N / sum(self.child_N) p_delta = soft_n - self.child_prior p_rel = p_delta / self.child_prior # Dump out some statistics output = [] output.append("{q:.4f}\n".format(q=self.Q)) output.append(self.most_visited_path()) output.append( "move: action Q U P P-Dir N soft-N" + " p-delta p-rel\n") output.append( "\n".join(["{!s:6}: {: .3f}, {: .3f}, {:.3f}, {:.3f}, {:.3f}, {:4d} {:.4f} {: .5f} {: .2f}".format( coords.to_kgs(self.board_size, coords.from_flat(self.board_size, key)), self.child_action_score[key], self.child_Q[key], self.child_U[key], self.child_prior[key], self.original_prior[key], int(self.child_N[key]), soft_n[key], p_delta[key], p_rel[key]) for key in sort_order][:15])) return "".join(output)