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"""
MCTS Core Module - Deterministic, testable Monte Carlo Tree Search implementation.
Features:
- Seeded RNG for deterministic behavior
- Progressive widening to control branching factor
- Simulation result caching with hashable state keys
- Clear separation of MCTS phases: select, expand, simulate, backpropagate
- Support for parallel rollouts with asyncio.Semaphore
"""
from __future__ import annotations
import asyncio
import hashlib
from collections import OrderedDict
from collections.abc import Callable
from dataclasses import dataclass, field
from typing import Any
import numpy as np
from .policies import RolloutPolicy, SelectionPolicy, ucb1
@dataclass
class MCTSState:
"""Hashable state representation for caching."""
state_id: str
features: dict[str, Any] = field(default_factory=dict)
def to_hash_key(self) -> str:
"""Generate a hashable key for this state."""
# Sort features for deterministic hashing
feature_str = str(sorted(self.features.items()))
combined = f"{self.state_id}:{feature_str}"
return hashlib.sha256(combined.encode()).hexdigest()
class MCTSNode:
"""
Monte Carlo Tree Search node with proper state management.
Attributes:
state: The state this node represents
parent: Parent node (None for root)
action: Action taken to reach this node from parent
children: List of child nodes
visits: Number of times this node has been visited
value_sum: Total accumulated value from simulations
rng: Seeded random number generator for deterministic behavior
"""
def __init__(
self,
state: MCTSState,
parent: MCTSNode | None = None,
action: str | None = None,
rng: np.random.Generator | None = None,
):
self.state = state
self.parent = parent
self.action = action
self.children: list[MCTSNode] = []
self.visits: int = 0
self.value_sum: float = 0.0
self.terminal: bool = False
self.expanded_actions: set = set()
self.available_actions: list[str] = []
# Track depth for O(1) tree statistics
self.depth: int = 0 if parent is None else parent.depth + 1
# Use provided RNG or create default
self._rng = rng or np.random.default_rng()
@property
def value(self) -> float:
"""Average value of this node."""
if self.visits == 0:
return 0.0
return self.value_sum / self.visits
@property
def is_fully_expanded(self) -> bool:
"""Check if all available actions have been expanded."""
return len(self.expanded_actions) >= len(self.available_actions)
def select_child(self, exploration_weight: float = 1.414) -> MCTSNode:
"""
Select best child using UCB1 policy.
Args:
exploration_weight: Exploration constant (c in UCB1)
Returns:
Best child node according to UCB1
"""
if not self.children:
raise ValueError("No children to select from")
best_child = None
best_score = float("-inf")
for child in self.children:
score = ucb1(
value_sum=child.value_sum,
visits=child.visits,
parent_visits=self.visits,
c=exploration_weight,
)
if score > best_score:
best_score = score
best_child = child
return best_child
def add_child(self, action: str, child_state: MCTSState) -> MCTSNode:
"""
Add a child node for the given action.
Args:
action: Action taken to reach child state
child_state: State of the child node
Returns:
Newly created child node
"""
child = MCTSNode(
state=child_state,
parent=self,
action=action,
rng=self._rng,
)
self.children.append(child)
self.expanded_actions.add(action)
return child
def get_unexpanded_action(self) -> str | None:
"""Get a random unexpanded action."""
unexpanded = [a for a in self.available_actions if a not in self.expanded_actions]
if not unexpanded:
return None
return self._rng.choice(unexpanded)
def __repr__(self) -> str:
return (
f"MCTSNode(state={self.state.state_id}, "
f"visits={self.visits}, value={self.value:.3f}, "
f"children={len(self.children)})"
)
class MCTSEngine:
"""
Main MCTS engine with deterministic behavior and advanced features.
Features:
- Seeded RNG for reproducibility
- Progressive widening to control branching
- Simulation result caching
- Parallel rollout support with semaphore
"""
def __init__(
self,
seed: int = 42,
exploration_weight: float = 1.414,
progressive_widening_k: float = 1.0,
progressive_widening_alpha: float = 0.5,
max_parallel_rollouts: int = 4,
cache_size_limit: int = 10000,
):
"""
Initialize MCTS engine.
Args:
seed: Random seed for deterministic behavior
exploration_weight: UCB1 exploration constant
progressive_widening_k: Progressive widening coefficient
progressive_widening_alpha: Progressive widening exponent
max_parallel_rollouts: Maximum concurrent rollouts
cache_size_limit: Maximum number of cached simulation results
"""
self.seed = seed
self.rng = np.random.default_rng(seed)
self.exploration_weight = exploration_weight
self.progressive_widening_k = progressive_widening_k
self.progressive_widening_alpha = progressive_widening_alpha
# Parallel rollout control
self.max_parallel_rollouts = max_parallel_rollouts
self._semaphore: asyncio.Semaphore | None = None
# Simulation cache: state_hash -> (value, visit_count)
# Using OrderedDict for LRU eviction
self._simulation_cache: OrderedDict[str, tuple[float, int]] = OrderedDict()
self.cache_size_limit = cache_size_limit
# Statistics
self.total_simulations = 0
self.cache_hits = 0
self.cache_misses = 0
self.cache_evictions = 0
# Cached tree statistics for O(1) retrieval
self._cached_tree_depth: int = 0
self._cached_node_count: int = 0
def reset_seed(self, seed: int) -> None:
"""Reset the random seed for new experiment."""
self.seed = seed
self.rng = np.random.default_rng(seed)
def clear_cache(self) -> None:
"""Clear simulation result cache."""
self._simulation_cache.clear()
self.cache_hits = 0
self.cache_misses = 0
self.cache_evictions = 0
def should_expand(self, node: MCTSNode) -> bool:
"""
Check if node should expand based on progressive widening.
Progressive widening formula: expand when visits > k * n^alpha
where n is the number of children.
This prevents excessive branching and focuses search on promising areas.
"""
if node.terminal or node.is_fully_expanded:
return False
num_children = len(node.children)
threshold = self.progressive_widening_k * (num_children**self.progressive_widening_alpha)
return node.visits > threshold
def select(self, node: MCTSNode) -> MCTSNode:
"""
MCTS Selection Phase: traverse tree to find leaf node.
Uses UCB1 to balance exploration and exploitation.
"""
while node.children and not node.terminal:
# Check if we should expand instead of selecting
if self.should_expand(node):
break
node = node.select_child(self.exploration_weight)
return node
def expand(
self,
node: MCTSNode,
action_generator: Callable[[MCTSState], list[str]],
state_transition: Callable[[MCTSState, str], MCTSState],
) -> MCTSNode:
"""
MCTS Expansion Phase: add a new child node.
Args:
node: Node to expand
action_generator: Function to generate available actions
state_transition: Function to compute next state from action
Returns:
Newly expanded child node, or original node if cannot expand
"""
if node.terminal:
return node
# Generate available actions if not yet done
if not node.available_actions:
node.available_actions = action_generator(node.state)
if not node.available_actions:
node.terminal = True
return node
# Check progressive widening
if not self.should_expand(node):
return node
# Get unexpanded action
action = node.get_unexpanded_action()
if action is None:
return node
# Create child state
child_state = state_transition(node.state, action)
child = node.add_child(action, child_state)
# Update cached node count for O(1) retrieval
self._cached_node_count += 1
return child
async def simulate(
self,
node: MCTSNode,
rollout_policy: RolloutPolicy,
max_depth: int = 10,
) -> float:
"""
MCTS Simulation Phase: evaluate node value through rollout.
Uses caching to avoid redundant simulations.
Args:
node: Node to simulate from
rollout_policy: Policy for rollout evaluation
max_depth: Maximum rollout depth
Returns:
Estimated value from simulation
"""
# Check cache first
state_hash = node.state.to_hash_key()
if state_hash in self._simulation_cache:
cached_value, cached_count = self._simulation_cache[state_hash]
# Move to end for LRU (most recently used)
self._simulation_cache.move_to_end(state_hash)
self.cache_hits += 1
# Return cached average with small noise for exploration
noise = self.rng.normal(0, 0.01)
return cached_value + noise
self.cache_misses += 1
# Acquire semaphore for parallel control
if self._semaphore is None:
self._semaphore = asyncio.Semaphore(self.max_parallel_rollouts)
async with self._semaphore:
# Perform rollout
value = await rollout_policy.evaluate(
state=node.state,
rng=self.rng,
max_depth=max_depth,
)
self.total_simulations += 1
# Update cache with LRU eviction
if state_hash in self._simulation_cache:
# Update existing cache entry with running average
old_value, old_count = self._simulation_cache[state_hash]
new_count = old_count + 1
new_value = (old_value * old_count + value) / new_count
self._simulation_cache[state_hash] = (new_value, new_count)
# Move to end for LRU (most recently used)
self._simulation_cache.move_to_end(state_hash)
else:
# Evict oldest entry if cache is full
if len(self._simulation_cache) >= self.cache_size_limit:
# Remove the first item (least recently used)
self._simulation_cache.popitem(last=False)
self.cache_evictions += 1
# Add new entry at the end (most recently used)
self._simulation_cache[state_hash] = (value, 1)
return value
def backpropagate(self, node: MCTSNode, value: float) -> None:
"""
MCTS Backpropagation Phase: update ancestor statistics.
Args:
node: Leaf node to start backpropagation
value: Value to propagate up the tree
"""
# Update cached tree depth if this node is deeper than current max
if node.depth > self._cached_tree_depth:
self._cached_tree_depth = node.depth
current = node
while current is not None:
current.visits += 1
current.value_sum += value
current = current.parent
async def run_iteration(
self,
root: MCTSNode,
action_generator: Callable[[MCTSState], list[str]],
state_transition: Callable[[MCTSState, str], MCTSState],
rollout_policy: RolloutPolicy,
max_rollout_depth: int = 10,
) -> None:
"""
Run a single MCTS iteration (select, expand, simulate, backpropagate).
Args:
root: Root node of the tree
action_generator: Function to generate actions
state_transition: Function to compute state transitions
rollout_policy: Policy for rollout evaluation
max_rollout_depth: Maximum depth for rollouts
"""
# Selection
leaf = self.select(root)
# Expansion
if not leaf.terminal and leaf.visits > 0:
leaf = self.expand(leaf, action_generator, state_transition)
# Simulation
value = await self.simulate(leaf, rollout_policy, max_rollout_depth)
# Backpropagation
self.backpropagate(leaf, value)
async def search(
self,
root: MCTSNode,
num_iterations: int,
action_generator: Callable[[MCTSState], list[str]],
state_transition: Callable[[MCTSState, str], MCTSState],
rollout_policy: RolloutPolicy,
max_rollout_depth: int = 10,
selection_policy: SelectionPolicy = SelectionPolicy.MAX_VISITS,
) -> tuple[str | None, dict[str, Any]]:
"""
Run MCTS search for specified number of iterations.
Args:
root: Root node to search from
num_iterations: Number of MCTS iterations
action_generator: Function to generate available actions
state_transition: Function to compute state transitions
rollout_policy: Policy for rollout simulation
max_rollout_depth: Maximum rollout depth
selection_policy: Policy for final action selection
Returns:
Tuple of (best_action, statistics_dict)
"""
# Reset cached tree statistics for new search
self._cached_tree_depth = 0
self._cached_node_count = 1 # Start with root node
# Initialize root's available actions
if not root.available_actions:
root.available_actions = action_generator(root.state)
# Run iterations
for _i in range(num_iterations):
await self.run_iteration(
root=root,
action_generator=action_generator,
state_transition=state_transition,
rollout_policy=rollout_policy,
max_rollout_depth=max_rollout_depth,
)
# Select best action based on policy
best_action = self._select_best_action(root, selection_policy)
# Compute statistics
stats = self._compute_statistics(root, num_iterations)
return best_action, stats
def _select_best_action(
self,
root: MCTSNode,
policy: SelectionPolicy,
) -> str | None:
"""
Select the best action from root based on selection policy.
Args:
root: Root node with children
policy: Selection policy to use
Returns:
Best action string or None if no children
"""
if not root.children:
return None
if policy == SelectionPolicy.MAX_VISITS:
# Most robust: select action with most visits
best_child = max(root.children, key=lambda c: c.visits)
elif policy == SelectionPolicy.MAX_VALUE:
# Greedy: select action with highest average value
best_child = max(root.children, key=lambda c: c.value)
elif policy == SelectionPolicy.ROBUST_CHILD:
# Robust: require both high visits and high value
# Normalize both metrics and combine
max_visits = max(c.visits for c in root.children)
max_value = max(c.value for c in root.children) or 1.0
def robust_score(child):
visit_score = child.visits / max_visits if max_visits > 0 else 0
value_score = child.value / max_value if max_value > 0 else 0
return 0.5 * visit_score + 0.5 * value_score
best_child = max(root.children, key=robust_score)
else:
# Default to max visits
best_child = max(root.children, key=lambda c: c.visits)
return best_child.action
def _compute_statistics(
self,
root: MCTSNode,
num_iterations: int,
) -> dict[str, Any]:
"""
Compute comprehensive MCTS statistics.
Args:
root: Root node
num_iterations: Number of iterations run
Returns:
Dictionary of statistics
"""
# Best child info
best_child = None
if root.children:
best_child = max(root.children, key=lambda c: c.visits)
# Action statistics
action_stats = {}
for child in root.children:
action_stats[child.action] = {
"visits": child.visits,
"value": child.value,
"value_sum": child.value_sum,
"num_children": len(child.children),
}
return {
"iterations": num_iterations,
"root_visits": root.visits,
"root_value": root.value,
"num_children": len(root.children),
"best_action": best_child.action if best_child else None,
"best_action_visits": best_child.visits if best_child else 0,
"best_action_value": best_child.value if best_child else 0.0,
"action_stats": action_stats,
"total_simulations": self.total_simulations,
"cache_hits": self.cache_hits,
"cache_misses": self.cache_misses,
"cache_evictions": self.cache_evictions,
"cache_hit_rate": (
self.cache_hits / (self.cache_hits + self.cache_misses)
if (self.cache_hits + self.cache_misses) > 0
else 0.0
),
"cache_size": len(self._simulation_cache),
"seed": self.seed,
}
def get_tree_depth(self, node: MCTSNode) -> int:
"""Get maximum depth of the tree from given node.
Uses iterative BFS to avoid stack overflow for large trees (5000+ nodes).
Each level of the tree is processed iteratively, tracking depth as we go.
"""
if not node.children:
return 0
from collections import deque
max_depth = 0
# Queue contains tuples of (node, depth)
queue = deque([(node, 0)])
while queue:
current_node, depth = queue.popleft()
max_depth = max(max_depth, depth)
for child in current_node.children:
queue.append((child, depth + 1))
return max_depth
def count_nodes(self, node: MCTSNode) -> int:
"""Count total number of nodes in tree.
Uses iterative BFS to avoid stack overflow for large trees (5000+ nodes).
Traverses all nodes in the tree using a queue-based approach.
"""
from collections import deque
count = 0
queue = deque([node])
while queue:
current_node = queue.popleft()
count += 1
for child in current_node.children:
queue.append(child)
return count
def get_cached_tree_depth(self) -> int:
"""
Get cached maximum tree depth in O(1) time.
Returns:
Maximum depth of tree from last search
"""
return self._cached_tree_depth
def get_cached_node_count(self) -> int:
"""
Get cached total node count in O(1) time.
Returns:
Total number of nodes in tree from last search
"""
return self._cached_node_count
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