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# Copyright 2018 Google LLC
#
# 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.
"""
import collections
import math
from absl import flags
import numpy as np
import coords
import go
# 722 moves for 19x19, 162 for 9x9
flags.DEFINE_integer('max_game_length', int(go.N ** 2 * 2),
'Move number at which game is forcibly terminated')
flags.DEFINE_float('c_puct_base', 19652,
'Exploration constants balancing priors vs. value net output.')
flags.DEFINE_float('c_puct_init', 1.25,
'Exploration constants balancing priors vs. value net output.')
flags.DEFINE_float('dirichlet_noise_alpha', 0.03 * 361 / (go.N ** 2),
'Concentrated-ness of the noise being injected into priors.')
flags.register_validator('dirichlet_noise_alpha', lambda x: 0 <= x < 1)
flags.DEFINE_float('dirichlet_noise_weight', 0.25,
'How much to weight the priors vs. dirichlet noise when mixing')
flags.register_validator('dirichlet_noise_weight', lambda x: 0 <= x < 1)
FLAGS = flags.FLAGS
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):
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 flattened coord
(raw number between 0-N^2, with None a pass)
parent: A parent MCTSNode.
"""
def __init__(self, position, fmove=None, parent=None):
if parent is None:
parent = DummyNode()
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 = 1 - self.position.all_legal_moves()
self.child_N = np.zeros([go.N * go.N + 1], dtype=np.float32)
self.child_W = np.zeros([go.N * go.N + 1], dtype=np.float32)
# save a copy of the original prior before it gets mutated by d-noise.
self.original_prior = np.zeros([go.N * go.N + 1], dtype=np.float32)
self.child_prior = np.zeros([go.N * go.N + 1], dtype=np.float32)
self.children = {} # map of flattened moves to resulting MCTSNode
def __repr__(self):
return "<MCTSNode move=%s, N=%s, to_play=%s>" % (
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 - 1000 * self.illegal_moves)
@property
def child_Q(self):
return self.child_W / (1 + self.child_N)
@property
def child_U(self):
return ((2.0 * (math.log(
(1.0 + self.N + FLAGS.c_puct_base) / FLAGS.c_puct_base)
+ FLAGS.c_puct_init)) * math.sqrt(max(1, self.N - 1)) *
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 = go.N * go.N
while True:
# 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):
"""Adds 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(fcoord))
self.children[fcoord] = MCTSNode(
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 incorporate_results(self, move_probabilities, value, up_to):
assert move_probabilities.shape == (go.N * go.N + 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 a node was picked multiple times (despite vlosses), we shouldn't
# expand it more than once.
if self.is_expanded:
return
self.is_expanded = True
# Zero out illegal moves.
move_probs = move_probabilities * (1 - self.illegal_moves)
scale = sum(move_probs)
if scale > 0:
# Re-normalize move_probabilities.
move_probs *= 1 / scale
self.original_prior = self.child_prior = move_probs
# 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([go.N * go.N + 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.N += 1
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."""
return self.position.is_game_over() or self.position.n >= FLAGS.max_game_length
def inject_noise(self):
epsilon = 1e-5
legal_moves = (1 - self.illegal_moves) + epsilon
a = legal_moves * ([FLAGS.dirichlet_noise_alpha] * (go.N * go.N + 1))
dirichlet = np.random.dirichlet(a)
self.child_prior = (self.child_prior * (1 - FLAGS.dirichlet_noise_weight) +
dirichlet * FLAGS.dirichlet_noise_weight)
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 ** .98
sum_probs = np.sum(probs)
if sum_probs == 0:
return probs
return probs / np.sum(probs)
def best_child(self):
# Sort by child_N tie break with action score.
return np.argmax(self.child_N + self.child_action_score / 10000)
def most_visited_path_nodes(self):
node = self
output = []
while node.children:
node = node.children.get(node.best_child())
assert node is not None
output.append(node)
return output
def most_visited_path(self):
output = []
node = self
for node in self.most_visited_path_nodes():
output.append("%s (%d) ==> " % (
coords.to_gtp(coords.from_flat(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..."""
output = []
for node in self.most_visited_path_nodes():
if max(node.child_N) <= 1:
break
output.append(coords.to_gtp(coords.from_flat(node.fmove)))
return ' '.join(output)
def rank_children(self):
ranked_children = list(range(go.N * go.N + 1))
ranked_children.sort(key=lambda i: (
self.child_N[i], self.child_action_score[i]), reverse=True)
return ranked_children
def describe(self):
ranked_children = self.rank_children()
soft_n = self.child_N / max(1, sum(self.child_N))
prior = self.child_prior
p_delta = soft_n - prior
p_rel = np.divide(p_delta, prior, out=np.zeros_like(
p_delta), where=prior != 0)
# 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")
for i in ranked_children[:15]:
if self.child_N[i] == 0:
break
output.append("\n{!s:4} : {: .3f} {: .3f} {:.3f} {:.3f} {:.3f} {:5d} {:.4f} {: .5f} {: .2f}".format(
coords.to_gtp(coords.from_flat(i)),
self.child_action_score[i],
self.child_Q[i],
self.child_U[i],
self.child_prior[i],
self.original_prior[i],
int(self.child_N[i]),
soft_n[i],
p_delta[i],
p_rel[i]))
return ''.join(output)