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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.
#include "cc/mcts_tree.h"
#include <emmintrin.h>
#include <algorithm>
#include <cmath>
#include <functional>
#include <tuple>
#include <utility>
#include "absl/strings/str_format.h"
#include "absl/types/optional.h"
#include "cc/algorithm.h"
#include "cc/logging.h"
namespace minigo {
namespace {
// Superko implementation that uses MctsNode::superko_cache.
class ZobristHistory : public Position::ZobristHistory {
public:
explicit ZobristHistory(const MctsNode* node) : node_(node) {}
bool HasPositionBeenPlayedBefore(zobrist::Hash stone_hash) const {
for (const auto* node = node_; node != nullptr; node = node->parent) {
if (node->superko_cache != nullptr) {
return node->superko_cache->contains(stone_hash);
} else {
if (node->position.stone_hash() == stone_hash) {
return true;
}
}
}
return false;
}
private:
const MctsNode* node_;
};
absl::optional<symmetry::Symmetry> CalculateCanonicalSymmetry(
const Position& position) {
// TODO(tommadams): skip this check if `move` is kPass or on the diagonal.
static_assert(symmetry::kIdentity == 0, "kIdentity must be 0");
// When choosing a canonical symmetry, we consider the "best" symmetry to
// be the one with the smallest Zobrist hash. The "best" symmetry is only
// canonical if its hash value is also unique among the hashes from the
// other possible symmetries.
auto best_symmetry = symmetry::kIdentity;
auto best_hash = position.stone_hash();
bool found_unique_hash = true;
std::array<Stone, kN * kN> transformed;
for (int i = 1; i < symmetry::kNumSymmetries; ++i) {
auto sym = static_cast<symmetry::Symmetry>(i);
symmetry::ApplySymmetry<kN, 1>(sym, position.stones().data(),
transformed.data());
auto stone_hash = Position::CalculateStoneHash(transformed);
if (stone_hash < best_hash) {
best_symmetry = sym;
best_hash = stone_hash;
} else if (stone_hash == best_hash) {
found_unique_hash = false;
break;
}
}
if (found_unique_hash) {
return symmetry::Inverse(best_symmetry);
}
return absl::nullopt;
}
constexpr int kSuperKoCacheStride = 8;
} // namespace
MctsNode::MctsNode(EdgeStats* stats, const Position& position)
: parent(nullptr),
stats(stats),
stats_idx(0),
move(Coord::kInvalid),
is_expanded(false),
has_canonical_symmetry(false),
position(position) {}
MctsNode::MctsNode(MctsNode* parent, Coord move)
: parent(parent),
stats(&parent->edges),
stats_idx(move),
move(move),
is_expanded(false),
has_canonical_symmetry(parent->has_canonical_symmetry),
canonical_symmetry(parent->canonical_symmetry),
position(parent->position) {
// TODO(tommadams): move this code into the MctsTree and only perform it
// only if we are using an inference cache.
if (!has_canonical_symmetry) {
auto sym = CalculateCanonicalSymmetry(position);
if (sym.has_value()) {
has_canonical_symmetry = true;
canonical_symmetry = sym.value();
}
}
MG_DCHECK(move >= 0);
MG_DCHECK(move < kNumMoves);
ZobristHistory zobrist_history(this);
position.PlayMove(move, position.to_play(), &zobrist_history);
// Insert a cache of ancestor Zobrist hashes at regular depths in the tree.
// See the comment for superko_cache in the mcts_node.h for more details.
if ((position.n() % kSuperKoCacheStride) == 0) {
superko_cache = absl::make_unique<SuperkoCache>();
superko_cache->reserve(position.n() + 1);
superko_cache->insert(position.stone_hash());
for (auto* node = parent; node != nullptr; node = node->parent) {
if (node->superko_cache != nullptr) {
superko_cache->insert(node->superko_cache->begin(),
node->superko_cache->end());
break;
}
superko_cache->insert(node->position.stone_hash());
}
}
}
Coord MctsNode::GetMostVisitedMove(bool restrict_pass_alive) const {
// Find the set of moves with the largest N.
inline_vector<Coord, kNumMoves> moves;
// CalculatePassAliveRegions does not include the kPass point.
std::array<Color, kN * kN> out_of_bounds;
if (restrict_pass_alive) {
out_of_bounds = position.CalculatePassAliveRegions();
} else {
for (auto& x : out_of_bounds) {
x = Color::kEmpty;
}
}
int best_N = 0;
for (int i = 0; i < kNumMoves; ++i) {
if ((i != Coord::kPass) && (out_of_bounds[i] != Color::kEmpty)) {
continue;
}
int cn = child_N(i);
if (cn >= best_N) {
if (cn > best_N) {
moves.clear();
best_N = cn;
}
moves.push_back(i);
}
}
if (moves.empty()) {
return Coord::kPass;
}
// If there's only one move with the largest N, we're done.
if (moves.size() == 1) {
return moves[0];
}
// Otherwise, break tie using the child action score.
float to_play = position.to_play() == Color::kBlack ? 1 : -1;
float U_common = U_scale() * std::sqrt(1.0f + N());
Coord c = moves[0];
float best_cas =
CalculateSingleMoveChildActionScore(to_play, U_common, moves[0]);
for (int i = 0; i < moves.size(); ++i) {
float cas =
CalculateSingleMoveChildActionScore(to_play, U_common, moves[i]);
if (cas > best_cas) {
best_cas = cas;
c = moves[i];
}
}
return c;
}
std::vector<Coord> MctsNode::GetMostVisitedPath() const {
std::vector<Coord> path;
const auto* node = this;
while (!node->children.empty()) {
Coord c = node->GetMostVisitedMove();
if (node->child_N(c) == 0) {
// In cases where nodes have been added to the tree manually (after the
// user has played a move, loading an SGF game), it's possible that no
// children have been visited. Break before adding a spurious node to the
// path.
break;
}
path.push_back(c);
auto it = node->children.find(c);
if (it == node->children.end()) {
// When we reach the move limit, last node will have children with visit
// counts but no children.
break;
}
node = it->second.get();
}
return path;
}
std::string MctsNode::GetMostVisitedPathString() const {
std::string result;
const auto* node = this;
for (Coord c : GetMostVisitedPath()) {
auto it = node->children.find(c);
MG_CHECK(it != node->children.end());
node = it->second.get();
absl::StrAppendFormat(&result, "%s (%d) ==> ", node->move.ToGtp(),
node->N());
}
absl::StrAppendFormat(&result, "Q: %0.5f", node->Q());
return result;
}
void MctsNode::PruneChildren(Coord c) {
auto child = std::move(children[c]);
children.clear();
children[c] = std::move(child);
}
void MctsNode::ClearChildren() {
// I _think_ this is all the state we need to clear...
children.clear();
edges = {};
*stats = {};
is_expanded = false;
}
// Vectorized version of CalculateChildActionScore.
void MctsNode::CalculateChildActionScoreSse(PaddedSpan<float> result) const {
__m128 to_play = _mm_set_ps1(position.to_play() == Color::kBlack ? 1 : -1);
__m128 U_common =
_mm_set_ps1(U_scale() * std::sqrt(std::max<float>(1, N() - 1)));
// A couple of useful constants.
__m128i >
__m128 one_thousand = _mm_set_ps1(1000);
for (int i = 0; i < kNumMoves; i += 4) {
// `rcp_N_one = 1 / (1 + child_N(i))`
// The division is performed using an approximate reciprocal instruction
// that has a maximum relative error of 1.5 * 2^-12.
__m128i N =
_mm_loadu_si128(reinterpret_cast<const __m128i*>(edges.N.data() + i));
__m128 rcp_N_one = _mm_rcp_ps(_mm_cvtepi32_ps(_mm_add_epi32(one, N)));
// `Q = child_W(i) / (1 + child_N(i))`
__m128 W = _mm_loadu_ps(edges.W.data() + i);
__m128 Q = _mm_mul_ps(W, rcp_N_one);
// `U = U_common * child_P(i) / (1 + child_N(i))`
__m128 P = _mm_loadu_ps(edges.P.data() + i);
__m128 U = _mm_mul_ps(_mm_mul_ps(U_common, P), rcp_N_one);
// `legal_bits = position.legal_move(i)`
// This requires a few instructions to load the legal move bytes and
// shuffle them into each of the four vector slots.
__m128i legal_bits = _mm_loadu_si128(
reinterpret_cast<const __m128i*>(position.legal_moves().data() + i));
legal_bits = _mm_unpacklo_epi8(legal_bits, _mm_setzero_si128());
legal_bits = _mm_unpacklo_epi16(legal_bits, _mm_setzero_si128());
// `legal = legal_bits == 0 ? 1000 : 0`
__m128 legal =
_mm_castsi128_ps(_mm_cmpeq_epi32(legal_bits, _mm_setzero_si128()));
legal = _mm_and_ps(legal, one_thousand);
// `child_action_score[i] = Q * to_play + U - legal`
__m128 cas = _mm_sub_ps(_mm_add_ps(_mm_mul_ps(Q, to_play), U), legal);
_mm_storeu_ps(result.data() + i, cas);
}
}
std::array<float, kNumMoves> MctsNode::CalculateChildActionScore() const {
float to_play = position.to_play() == Color::kBlack ? 1 : -1;
float U_common = U_scale() * std::sqrt(std::max<float>(1, N() - 1));
std::array<float, kNumMoves> result;
for (int i = 0; i < kNumMoves; ++i) {
result[i] = CalculateSingleMoveChildActionScore(to_play, U_common, i);
}
return result;
}
MctsNode* MctsNode::MaybeAddChild(Coord c) {
auto it = children.find(c);
if (it == children.end()) {
// TODO(tommadams): Allocate children out of a custom block allocator: we
// spend about 5% of our runtme inside MctsNode::PruneChildren freeing
// nodes.
it = children.emplace(c, absl::make_unique<MctsNode>(this, c)).first;
}
return it->second.get();
}
std::string MctsTree::Stats::ToString() const {
return absl::StrFormat(
"%d nodes, %d leaf, %.1f average children\n"
"%.1f average depth, %d max depth\n",
num_nodes, num_leaf_nodes,
1.0f * num_nodes / std::max(1, num_nodes - num_leaf_nodes),
1.0f * depth_sum / num_nodes, max_depth);
}
std::ostream& operator<<(std::ostream& os, const MctsTree::Options& options) {
return os << "value_init_penalty:" << options.value_init_penalty
<< " policy_softmax_temp:" << options.policy_softmax_temp
<< " soft_pick_enabled:" << options.soft_pick_enabled
<< " soft_pick_cutoff:" << options.soft_pick_cutoff;
}
MctsTree::MctsTree(const Position& position, const Options& options)
: game_root_(&game_root_stats_, position), options_(options) {
root_ = &game_root_;
}
MctsNode* MctsTree::SelectLeaf(bool allow_pass) {
auto* node = root_;
for (;;) {
// If a node has never been evaluated, we have no basis to select a child.
if (!node->is_expanded) {
return node;
}
PaddedArray<float, kNumMoves> child_action_score;
node->CalculateChildActionScoreSse(child_action_score);
if (!allow_pass) {
child_action_score[Coord::kPass] = -100000;
}
Coord best_move = ArgMaxSse(child_action_score);
if (!node->position.legal_move(best_move)) {
best_move = Coord::kPass;
}
node = node->MaybeAddChild(best_move);
}
}
Coord MctsTree::PickMove(Random* rnd, bool restrict_pass_alive) const {
if (options_.soft_pick_enabled &&
root_->position.n() < options_.soft_pick_cutoff) {
return SoftPickMove(rnd);
} else {
return PickMostVisitedMove(restrict_pass_alive);
}
}
void MctsTree::PlayMove(Coord c) {
MG_CHECK(!is_game_over() && is_legal_move(c))
<< c << " " << is_game_over() << " " << is_legal_move(c);
root_ = root_->MaybeAddChild(c);
// Don't need to keep the parent's children around anymore because we'll
// never revisit them during normal play.
// TODO(tommadams): we should just delete all ancestors. This will require
// changes to UndoMove though.
root_->parent->PruneChildren(c);
}
void MctsTree::AddVirtualLoss(MctsNode* leaf) {
auto* node = leaf;
for (;;) {
++node->num_virtual_losses_applied;
node->stats->W[node->stats_idx] +=
node->position.to_play() == Color::kBlack ? 1 : -1;
if (node == root_) {
return;
}
node = node->parent;
}
}
void MctsTree::RevertVirtualLoss(MctsNode* leaf) {
auto* node = leaf;
for (;;) {
--node->num_virtual_losses_applied;
node->stats->W[node->stats_idx] -=
node->position.to_play() == Color::kBlack ? 1 : -1;
if (node == root_) {
return;
}
node = node->parent;
}
}
void MctsTree::IncorporateResults(MctsNode* leaf,
absl::Span<const float> move_probabilities,
float value) {
MG_DCHECK(move_probabilities.size() == kNumMoves);
// A finished game should not be going through this code path, it should
// directly call BackupValue on the result of the game.
MG_DCHECK(!leaf->game_over());
// If the node has already been selected for the next inference batch, we
// shouldn't 'expand' it again.
if (leaf->is_expanded) {
return;
}
float policy_scalar = 0;
for (int i = 0; i < kNumMoves; ++i) {
if (leaf->position.legal_move(i)) {
policy_scalar += move_probabilities[i];
}
}
if (policy_scalar > std::numeric_limits<float>::min()) {
policy_scalar = 1 / policy_scalar;
}
// NOTE: Minigo uses value [-1, 1] from black's perspective
// Leela uses value [0, 1] from current player's perspective
// AlphaGo uses [0, 1] in tree search (see matthew lai's post)
//
// The initial value of a child's Q is not perfectly understood.
// There are a couple of general ideas:
// * Init to Parent:
// Init a new child to its parent value.
// We think of this as saying "The game is probably the same after
// *any* move".
// * Init to Draw AKA init to zero AKA "position looks even":
// Init a new child to 0 for {-1, 1} or 0.5 for LZ.
// We tested this in v11, because this is how we interpretted the
// original AGZ paper. This doesn't make a lot of sense: The losing
// player tends to explore every move before reading a second one
// twice. The winning player tends to read only the top policy move
// because it has much higher value than any other move.
// * Init to Parent minus a constant AKA FPU (Leela's approach):
// This outperformed init to parent in eval matches when LZ tested it.
// Leela-Zero uses a value around 0.15-0.25 based on policy of explored
// children. LCZero uses a much large value 1.25 (they use {-1 to 1}).
// * Init to Loss:
// Init all children to losing.
// We think of this as saying "Only a small number of moves work don't
// get distracted"
float reduction = options_.value_init_penalty *
(leaf->position.to_play() == Color::kBlack ? 1 : -1);
float reduced_value = std::min(1.0f, std::max(-1.0f, value - reduction));
leaf->is_expanded = true;
for (int i = 0; i < kNumMoves; ++i) {
// Zero out illegal moves, and re-normalize move_probabilities.
float move_prob = leaf->position.legal_move(i)
? policy_scalar * move_probabilities[i]
: 0;
leaf->edges.original_P[i] = leaf->edges.P[i] = move_prob;
// Note that we accumulate W here, rather than assigning.
// When performing tree search normally, we could just assign the value to W
// because the result of value head is known before we expand the node.
// When running Minigui in study move however, we load the entire game tree
// before starting background inference. This means that while background
// inferences are being performed, nodes in the tree may already be expanded
// and have non-zero W values at the time we need to incorporate a result
// for the node from the value head.
// TODO(tommadams): Minigui doesn't work this way any more so we can just
// assign.
leaf->edges.W[i] += reduced_value;
}
BackupValue(leaf, value);
}
void MctsTree::IncorporateEndGameResult(MctsNode* leaf, float value) {
MG_DCHECK(leaf->game_over());
MG_DCHECK(!leaf->is_expanded);
BackupValue(leaf, value);
}
void MctsTree::BackupValue(MctsNode* leaf, float value) {
auto* node = leaf;
for (;;) {
node->stats->W[node->stats_idx] += value;
node->stats->N[node->stats_idx] += 1;
if (node == root_) {
return;
}
node = node->parent;
}
}
void MctsTree::InjectNoise(const std::array<float, kNumMoves>& noise,
float mix) {
MG_CHECK(root_->is_expanded);
// NOTE: our interpretation is to only add dirichlet noise to legal moves.
// Because dirichlet entries are independent we can simply zero and rescale.
float scalar = 0;
for (int i = 0; i < kNumMoves; ++i) {
if (root_->position.legal_move(i)) {
scalar += noise[i];
}
}
if (scalar > std::numeric_limits<float>::min()) {
scalar = 1.0 / scalar;
}
for (int i = 0; i < kNumMoves; ++i) {
float scaled_noise =
scalar * (root_->position.legal_move(i) ? noise[i] : 0);
root_->edges.P[i] = (1 - mix) * root_->edges.P[i] + mix * scaled_noise;
}
}
void MctsTree::ReshapeFinalVisits(bool restrict_pass_alive) {
// Since we aren't actually disallowing *reads* of bensons moves, only their
// selection, we get the most visited move regardless of bensons status and
// reshape based on its action score.
Coord best = root_->GetMostVisitedMove(false);
MG_CHECK(root_->edges.N[best] > 0);
auto pass_alive_regions = root_->position.CalculatePassAliveRegions();
float U_common = root_->U_scale() * std::sqrt(1.0f + root_->N());
float to_play = root_->position.to_play() == Color::kBlack ? 1 : -1;
float best_cas = root_->CalculateSingleMoveChildActionScore(to_play, U_common,
uint16_t(best));
bool any = false; // Track if any move has visits after pruning.
// We explored this child with uncertainty about its value. Now, after
// searching, we change the visit count to reflect how many visits we would
// have given it with our newer understanding of its regret relative to our
// best move.
for (int i = 0; i < kNumMoves; ++i) {
// Remove visits in pass alive areas.
if (restrict_pass_alive && (i != Coord::kPass) &&
(pass_alive_regions[i] != Color::kEmpty)) {
root_->edges.N[i] = 0;
continue;
}
// Skip the best move; it has the highest action score.
if (i == best) {
if (root_->edges.N[i] > 0) {
any = true;
}
continue;
}
// Change N_child to the smallest value that satisfies the inequality
// best_cas > Q + (U_scale * P * sqrt(N_parent) / N_child)
// Solving for N_child, we get:
int new_N = std::max<int>(
0, std::min<int>(root_->child_N(i),
-1 *
(root_->U_scale() * root_->child_P(i) *
std::sqrt(root_->N())) /
((root_->child_Q(i) * to_play) - best_cas)));
root_->edges.N[i] = new_N;
if (root_->edges.N[i] > 0) {
any = true;
}
}
// If all visits were in bensons regions, put a visit on pass.
if (!any) {
root_->edges.N[Coord::kPass] = 1;
}
}
std::array<float, kNumMoves> MctsTree::CalculateSearchPi() const {
std::array<float, kNumMoves> search_pi;
if (options_.soft_pick_enabled &&
root_->position.n() < options_.soft_pick_cutoff) {
// Squash counts before normalizing to match softpick behavior in PickMove.
for (int i = 0; i < kNumMoves; ++i) {
search_pi[i] = std::pow(root_->child_N(i), options_.policy_softmax_temp);
}
} else {
for (int i = 0; i < kNumMoves; ++i) {
search_pi[i] = root_->child_N(i);
}
}
// Normalize counts.
float sum = 0;
for (int i = 0; i < kNumMoves; ++i) {
sum += search_pi[i];
}
MG_CHECK(sum > 0);
for (int i = 0; i < kNumMoves; ++i) {
search_pi[i] /= sum;
}
return search_pi;
}
MctsTree::Stats MctsTree::CalculateStats() const {
Stats stats;
9E04
std::function<void(const MctsNode&, int)> traverse = [&](const MctsNode& node,
int depth) {
stats.num_nodes += 1;
stats.num_leaf_nodes += node.N() <= 1;
stats.max_depth = std::max(depth, stats.max_depth);
stats.depth_sum += depth;
for (const auto& child : node.children) {
traverse(*child.second.get(), depth + 1);
}
};
traverse(*root_, 0);
return stats;
}
std::string MctsTree::Describe() const {
auto sorted_move_info = CalculateRankedMoveInfo();
auto result = absl::StrFormat(
"%0.4f\n%s\n"
"move : action Q U P P-Dir N soft-N p-delta p-rel",
root_->Q(), root_->GetMostVisitedPathString());
float child_N_sum = 0;
for (const auto& N : root_->edges.N) {
child_N_sum += N;
}
for (int rank = 0; rank < 15; ++rank) {
Coord c = sorted_move_info[rank].c;
float soft_N = root_->child_N(c) / child_N_sum;
float p_delta = soft_N - root_->child_P(c);
float p_rel = p_delta / root_->child_P(c);
absl::StrAppendFormat(
&result,
"\n%-5s: % 4.3f % 4.3f %0.3f %0.3f %0.3f %5d %0.4f % 6.5f % 3.2f",
c.ToGtp(), sorted_move_info[rank].action_score, root_->child_Q(c),
root_->child_U(c), root_->child_P(c), root_->child_original_P(c),
root_->child_N(c), soft_N, p_delta, p_rel);
}
return result;
}
std::array<MctsTree::MoveInfo, kNumMoves> MctsTree::CalculateRankedMoveInfo()
const {
auto child_action_score = root_->CalculateChildActionScore();
std::array<MoveInfo, kNumMoves> move_info;
for (int i = 0; i < kNumMoves; ++i) {
move_info[i].c = i;
move_info[i].N = root_->child_N(i);
move_info[i].P = root_->child_P(i);
move_info[i].action_score = child_action_score[i];
}
std::sort(move_info.begin(), move_info.end(),
[](const MoveInfo& a, const MoveInfo& b) {
if (a.N != b.N) {
return a.N > b.N;
}
if (a.P != b.P) {
return a.P > b.P;
}
return a.action_score > b.action_score;
});
return move_info;
}
bool MctsTree::UndoMove() {
if (root_ == &game_root_) {
return false;
}
root_ = root_->parent;
return true;
}
Coord MctsTree::PickMostVisitedMove(bool restrict_pass_alive) const {
auto c = root_->GetMostVisitedMove(restrict_pass_alive);
if (!root_->position.legal_move(c)) {
c = Coord::kPass;
}
return c;
}
// SoftPickMove is only called for the opening moves of the game, so we don't
// bother restricting play in pass-alive territory.
Coord MctsTree::SoftPickMove(Random* rnd) const {
// Select from the first kN * kN moves (instead of kNumMoves) to avoid
// randomly choosing to pass early on in the game.
std::array<float, kN * kN> cdf;
// For moves before the temperature cutoff, exponentiate the probabilities by
// a temperature slightly larger than unity to encourage diversity in early
// play and hopefully to move away from 3-3s.
for (size_t i = 0; i < cdf.size(); ++i) {
cdf[i] = std::pow(root_->child_N(i), options_.policy_softmax_temp);
}
for (size_t i = 1; i < cdf.size(); ++i) {
cdf[i] += cdf[i - 1];
}
if (cdf.back() == 0) {
// It's actually possible for an early model to put all its reads into pass,
// in which case the SearchSorted call below will always return 0. In this
// case, we'll just let the model have its way and allow a pass.
return Coord::kPass;
}
Coord c = rnd->SampleCdf(absl::MakeSpan(cdf));
MG_DCHECK(root_->child_N(c) != 0);
return c;
}
} // namespace minigo