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"""
Neural-Guided Monte Carlo Tree Search (MCTS).
Implements AlphaZero-style MCTS with:
- Policy and value network guidance
- PUCT (Predictor + UCT) selection
- Dirichlet noise for exploration
- Virtual loss for parallel search
- Temperature-based action selection
Based on:
- "Mastering the Game of Go with Deep Neural Networks and Tree Search" (AlphaGo)
- "Mastering Chess and Shogi by Self-Play with a General RL Algorithm" (AlphaZero)
"""
from __future__ import annotations
import math
from collections.abc import Callable
from dataclasses import dataclass
from typing import Any
import numpy as np
import torch
import torch.nn as nn
from ...training.system_config import MCTSConfig
@dataclass
class GameState:
"""
Abstract game/problem state interface.
Users should subclass this for their specific domain.
"""
def get_legal_actions(self) -> list[Any]:
"""Return list of legal actions from this state."""
raise NotImplementedError
def apply_action(self, action: Any) -> GameState:
"""Apply action and return new state."""
raise NotImplementedError
def is_terminal(self) -> bool:
"""Check if this is a terminal state."""
raise NotImplementedError
def get_reward(self, player: int = 1) -> float:
"""Get reward for the player (1 or -1)."""
raise NotImplementedError
def to_tensor(self) -> torch.Tensor:
"""Convert state to tensor for neural network input."""
raise NotImplementedError
def get_canonical_form(self, player: int) -> GameState: # noqa: ARG002
"""Get state from perspective of given player."""
return self
def get_hash(self) -> str:
"""Get unique hash for this state (for caching)."""
raise NotImplementedError
def action_to_index(self, action: Any) -> int:
"""
Map action to its index in the neural network's action space.
This method should return the index corresponding to the action
in the network's policy output vector.
Default implementation uses string-based mapping for Tic-Tac-Toe style
actions (e.g., "0,0" -> 0, "0,1" -> 1, etc.). Override this method
for custom action mappings.
Args:
action: The action to map
Returns:
Index in the action space (0 to action_size-1)
"""
# Default implementation for grid-based actions like "row,col"
if isinstance(action, str) and "," in action:
row, col = map(int, action.split(","))
# Assume 3x3 grid by default - override for different sizes
return row * 3 + col
# For other action types, assume they are already indices
return int(action)
class NeuralMCTSNode:
"""
MCTS node with neural network guidance.
Stores statistics for PUCT selection and backpropagation.
"""
def __init__(
self,
state: GameState,
parent: NeuralMCTSNode | None = None,
action: Any | None = None,
prior: float = 0.0,
):
self.state = state
self.parent = parent
self.action = action # Action that led to this node
self.prior = prior # Prior probability from policy network
# Statistics
self.visit_count: int = 0
self.value_sum: float = 0.0
self.virtual_loss: float = 0.0
# Children: action -> NeuralMCTSNode
self.children: dict[Any, NeuralMCTSNode] = {}
# Caching
self.is_expanded: bool = False
self.is_terminal: bool = state.is_terminal()
@property
def value(self) -> float:
"""Average value (Q-value) of this node."""
if self.visit_count == 0:
return 0.0
return self.value_sum / self.visit_count
def expand(
self,
policy_probs: np.ndarray,
valid_actions: list[Any],
):
"""
Expand node by creating children for all legal actions.
Args:
policy_probs: Prior probabilities from policy network
valid_actions: List of legal actions
"""
self.is_expanded = True
for action, prior in zip(valid_actions, policy_probs, strict=True):
if action not in self.children:
next_state = self.state.apply_action(action)
self.children[action] = NeuralMCTSNode(
state=next_state,
parent=self,
action=action,
prior=prior,
)
def select_child(self, c_puct: float) -> tuple[Any, NeuralMCTSNode]:
"""
Select best child using PUCT algorithm.
PUCT = Q(s,a) + c_puct * P(s,a) * sqrt(N(s)) / (1 + N(s,a))
Args:
c_puct: Exploration constant
Returns:
(action, child_node) tuple
"""
best_score = -float("inf")
best_action = None
best_child = None
# Precompute sqrt term for efficiency
sqrt_parent_visits = math.sqrt(self.visit_count)
for action, child in self.children.items():
# Q-value (average value)
q_value = child.value
# U-value (exploration bonus)
u_value = c_puct * child.prior * sqrt_parent_visits / (1 + child.visit_count + child.virtual_loss)
# PUCT score
puct_score = q_value + u_value
if puct_score > best_score:
best_score = puct_score
best_action = action
best_child = child
return best_action, best_child
def add_virtual_loss(self, virtual_loss: float):
"""Add virtual loss for parallel search."""
self.virtual_loss += virtual_loss
def revert_virtual_loss(self, virtual_loss: float):
"""Remove virtual loss after search completes."""
self.virtual_loss -= virtual_loss
def update(self, value: float):
"""Update node statistics with search result."""
self.visit_count += 1
self.value_sum += value
def get_action_probs(self, temperature: float = 1.0) -> dict[Any, float]:
"""
Get action selection probabilities based on visit counts.
Args:
temperature: Temperature parameter
- temperature -> 0: argmax (deterministic)
- temperature = 1: proportional to visits
- temperature -> inf: uniform
Returns:
Dictionary mapping actions to probabilities
"""
if not self.children:
return {}
if temperature == 0:
# Deterministic: select most visited
visits = {action: child.visit_count for action, child in self.children.items()}
max_visits = max(visits.values())
best_actions = [a for a, v in visits.items() if v == max_visits]
# Uniform over best actions
prob = 1.0 / len(best_actions)
return {a: (prob if a in best_actions else 0.0) for a in self.children}
# Temperature-scaled visits
visits = np.array([child.visit_count for child in self.children.values()])
actions = list(self.children.keys())
if temperature != 1.0:
visits = visits ** (1.0 / temperature)
# Normalize to probabilities
probs = visits / visits.sum()
return dict(zip(actions, probs, strict=True))
class NeuralMCTS:
"""
Neural-guided MCTS for decision making.
Combines tree search with neural network evaluation
using the AlphaZero algorithm.
"""
def __init__(
self,
policy_value_network: nn.Module,
config: MCTSConfig,
device: str = "cpu",
):
"""
Initialize neural MCTS.
Args:
policy_value_network: Network that outputs (policy, value)
config: MCTS configuration
device: Device for neural network
"""
self.network = policy_value_network
self.config = config
self.device = device
# Caching for network evaluations
self.cache: dict[str, tuple[np.ndarray, float]] = {}
self.cache_hits = 0
self.cache_misses = 0
def add_dirichlet_noise(
self,
policy_probs: np.ndarray,
epsilon: float | None = None,
alpha: float | None = None,
) -> np.ndarray:
"""
Add Dirichlet noise to policy for exploration (at root only).
Policy' = (1 - epsilon) * Policy + epsilon * Noise
Args:
policy_probs: Original policy probabilities
epsilon: Mixing parameter (defaults to config)
alpha: Dirichlet concentration parameter (defaults to config)
Returns:
Noised policy probabilities
"""
epsilon = epsilon or self.config.dirichlet_epsilon
alpha = alpha or self.config.dirichlet_alpha
noise = np.random.dirichlet([alpha] * len(policy_probs))
return (1 - epsilon) * policy_probs + epsilon * noise
@torch.no_grad()
async def evaluate_state(self, state: GameState, add_noise: bool = False) -> tuple[np.ndarray, float]:
"""
Evaluate state using neural network.
Args:
state: Game state to evaluate
add_noise: Whether to add Dirichlet noise (for root exploration)
Returns:
(policy_probs, value) tuple
"""
# Check cache
state_hash = state.get_hash()
if not add_noise and state_hash in self.cache:
self.cache_hits += 1
return self.cache[state_hash]
self.cache_misses += 1
# Get legal actions
legal_actions = state.get_legal_actions()
if not legal_actions:
return np.array([]), 0.0
# Convert state to tensor
state_tensor = state.to_tensor().unsqueeze(0).to(self.device)
# Network forward pass
policy_logits, value = self.network(state_tensor)
# Convert to numpy (detach to remove gradients)
policy_logits = policy_logits.squeeze(0).detach().cpu().numpy()
value = value.item()
# Proper action masking: Map legal actions to their indices in the action space
# Create a mask for legal actions
action_mask = np.full_like(policy_logits, -np.inf) # Mask all actions initially
action_indices = []
# Map legal actions to their network output indices
for action in legal_actions:
try:
action_idx = state.action_to_index(action)
if 0 <= action_idx < len(policy_logits):
action_mask[action_idx] = 0 # Unmask legal actions
action_indices.append(action_idx)
except (ValueError, IndexError, AttributeError) as e:
# Fallback: if action_to_index fails, use sequential mapping
print(f"Warning: action_to_index failed for action {action}: {e}")
action_indices = list(range(len(legal_actions)))
action_mask = np.full_like(policy_logits, -np.inf)
action_mask[action_indices] = 0
break
# Apply mask before softmax for numerical stability
masked_logits = policy_logits + action_mask
# Compute softmax over legal actions only
exp_logits = np.exp(masked_logits - np.max(masked_logits)) # Subtract max for stability
policy_probs_full = exp_logits / exp_logits.sum()
# Extract probabilities for legal actions in order
policy_probs = policy_probs_full[action_indices]
# Normalize to ensure probabilities sum to 1 (handle numerical errors)
if policy_probs.sum() > 0:
policy_probs = policy_probs / policy_probs.sum()
else:
# Fallback: uniform distribution over legal actions
policy_probs = np.ones(len(legal_actions)) / len(legal_actions)
# Add Dirichlet noise if requested (root exploration)
if add_noise:
policy_probs = self.add_dirichlet_noise(policy_probs)
# Cache result (without noise)
if not add_noise:
self.cache[state_hash] = (policy_probs, value)
return policy_probs, value
async def search(
self,
root_state: GameState,
num_simulations: int | None = None,
temperature: float = 1.0,
add_root_noise: bool = True,
) -> tuple[dict[Any, float], NeuralMCTSNode]:
"""
Run MCTS search from root state.
Args:
root_state: Initial state
num_simulations: Number of MCTS simulations
temperature: Temperature for action selection
add_root_noise: Whether to add Dirichlet noise to root
Returns:
(action_probs, root_node) tuple
"""
num_simulations = num_simulations or self.config.num_simulations
# Create root node
root = NeuralMCTSNode(state=root_state)
# Expand root
policy_probs, _ = await self.evaluate_state(root_state, add_noise=add_root_noise)
legal_actions = root_state.get_legal_actions()
root.expand(policy_probs, legal_actions)
# Run simulations
for _ in range(num_simulations):
await self._simulate(root)
# Get action probabilities
action_probs = root.get_action_probs(temperature)
return action_probs, root
async def _simulate(self, node: NeuralMCTSNode) -> float:
"""
Run single MCTS simulation (select, expand, evaluate, backpropagate).
Args:
node: Root node for this simulation
Returns:
Value from this simulation
"""
path: list[NeuralMCTSNode] = []
# Selection: traverse tree using PUCT
current = node
while current.is_expanded and not current.is_terminal:
# Add virtual loss for parallel search
current.add_virtual_loss(self.config.virtual_loss)
path.append(current)
# Select best child
_, current = current.select_child(self.config.c_puct)
# Add leaf to path
path.append(current)
current.add_virtual_loss(self.config.virtual_loss)
# Evaluate leaf node
if current.is_terminal:
# Terminal node: use game result
value = current.state.get_reward()
else:
# Non-terminal: expand and evaluate with network
policy_probs, value = await self.evaluate_state(current.state, add_noise=False)
if not current.is_expanded:
legal_actions = current.state.get_legal_actions()
current.expand(policy_probs, legal_actions)
# Backpropagate
for node_in_path in reversed(path):
node_in_path.update(value)
node_in_path.revert_virtual_loss(self.config.virtual_loss)
# Flip value for opponent
value = -value
return value
def select_action(
self,
action_probs: dict[Any, float],
temperature: float = 1.0,
deterministic: bool = False,
) -> Any:
"""
Select action from probability distribution.
Args:
action_probs: Action probability dictionary
temperature: Temperature (unused if deterministic=True)
deterministic: If True, select action with highest probability
Returns:
Selected action
"""
if not action_probs:
return None
actions = list(action_probs.keys())
probs = list(action_probs.values())
if deterministic or temperature == 0:
return actions[np.argmax(probs)]
# Sample from distribution
return np.random.choice(actions, p=probs)
def clear_cache(self):
"""Clear the evaluation cache."""
self.cache.clear()
self.cache_hits = 0
self.cache_misses = 0
def get_cache_stats(self) -> dict:
"""Get cache performance statistics."""
total = self.cache_hits + self.cache_misses
hit_rate = self.cache_hits / total if total > 0 else 0.0
return {
"cache_size": len(self.cache),
"cache_hits": self.cache_hits,
"cache_misses": self.cache_misses,
"hit_rate": hit_rate,
}
# Training data collection
@dataclass
class MCTSExample:
"""Training example from MCTS self-play."""
state: torch.Tensor # State representation
policy_target: np.ndarray # Target policy (visit counts)
value_target: float # Target value (game outcome)
player: int # Player to move (1 or -1)
class SelfPlayCollector:
"""
Collect training data from self-play games.
Uses MCTS to generate high-quality training examples.
"""
def __init__(
self,
mcts: NeuralMCTS,
config: MCTSConfig,
):
self.mcts = mcts
self.config = config
async def play_game(
self,
initial_state: GameState,
temperature_threshold: int | None = None,
) -> list[MCTSExample]:
"""
Play a single self-play game.
Args:
initial_state: Starting game state
temperature_threshold: Move number to switch to greedy play
Returns:
List of training examples from the game
"""
temperature_threshold = temperature_threshold or self.config.temperature_threshold
examples: list[MCTSExample] = []
state = initial_state
player = 1 # Current player (1 or -1)
move_count = 0
while not state.is_terminal():
# Determine temperature
temperature = (
self.config.temperature_init if move_count < temperature_threshold else self.config.temperature_final
)
# Run MCTS
action_probs, root = await self.mcts.search(state, temperature=temperature, add_root_noise=True)
# Store training example
# Convert action probs to array for all actions
probs = np.array(list(action_probs.values()))
examples.append(
MCTSExample(
state=state.to_tensor(),
policy_target=probs,
value_target=0.0, # Will be filled with game outcome
player=player,
)
)
# Select and apply action
action = self.mcts.select_action(action_probs, temperature=temperature)
state = state.apply_action(action)
# Switch player
player = -player
move_count += 1
# Get game outcome
outcome = state.get_reward()
# Assign values to examples
for example in examples:
# Value is from perspective of the player who made the move
example.value_target = outcome if example.player == 1 else -outcome
return examples
async def generate_batch(self, num_games: int, initial_state_fn: Callable[[], GameState]) -> list[MCTSExample]:
"""
Generate a batch of training examples from multiple games.
Args:
num_games: Number of games to play
initial_state_fn: Function that returns initial game state
Returns:
Combined list of training examples
"""
all_examples = []
for _ in range(num_games):
initial_state = initial_state_fn()
examples = await self.play_game(initial_state)
all_examples.extend(examples)
# Clear cache periodically
if len(self.mcts.cache) > 10000:
self.mcts.clear_cache()
return all_examples
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