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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 numpy as np
import collections
import random
import math
import coords
import go
MAX_DEPTH = (go.N ** 2) * 1.4 # 505 moves for 19x19, 113 for 9x9
# Exploration constant
c_PUCT = 1.38
# Dirichlet noise, as a function of go.N
def D_NOISE_ALPHA(): return 0.03 * 361 / (go.N ** 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):
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, 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 = 1000 * (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 - 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 = go.N * go.N
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):
""" 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.unflatten_coords(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 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 == (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 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([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.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 >= MAX_DEPTH
def inject_noise(self):
dirch = np.random.dirichlet([D_NOISE_ALPHA()] * ((go.N * go.N) + 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_human_coord(
coords.unflatten_coords(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_human_coord(
coords.unflatten_coords(node.fmove)))
return ' '.join(output)
def describe(self):
sort_order = list(range(go.N * go.N + 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_human_coord(coords.unflatten_coords(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)