// The expand policy determines how we choose a yet untried node among
// the existing untried nodes
// An untried node represents a move that was never part of a move
// sequence
// The expand policy in this MCTS implementation is to randomly select
// an untried node
private TicTacToeMCTSNode ExpandPolicy(TicTacToeMCTSNode node)
{
// Get the currently untried moves
IReadOnlyList <Pos> untriedMoves = node.UntriedMoves;
// Randomly select one of the untried moves
Pos move = untriedMoves[random.Next(untriedMoves.Count)];
// Make the untried move and return the respective node
return(node.MakeMove(move) as TicTacToeMCTSNode);
}
// Play a turn
public Pos Play(Board gameBoard, ref string log)
{
// Keep start time
DateTime startTime = DateTime.Now;
// What is my deadline?
DateTime deadline = startTime + TimeSpan.FromSeconds(timeToThink);
// Create the root node using the current table
TicTacToeMCTSNode root = new TicTacToeMCTSNode(gameBoard, Board.NoMove);
// The node to be selected for play
TicTacToeMCTSNode selected;
// A string builder to build our MCTS log
StringBuilder sb = new StringBuilder();
// Number of simulations performed
int simulations = 0;
// Run MCTS and keep improving statistics while we have time
while (DateTime.Now < deadline)
{
MCTS(root);
}
// Get the best move, i.e. the one with a higher win ratio
// (by setting k = 0)
selected = SelectMovePolicy(root, 0);
// Build our debug log and count number of simulations performed
foreach (AbstractMCTSNode <Pos, CellState> node in root.Children)
{
sb.AppendFormat("{0} -> {1:f4} ({2}/{3})\n",
node.Move,
node.Wins / (float)node.Playouts,
node.Wins,
node.Playouts);
simulations += node.Playouts;
}
// Add summary to the beginning of log
sb.Insert(0, string.Format(
"Selected {0} with ratio {1} after {2} simulations\n",
selected.Move,
selected.Wins / (float)selected.Playouts,
simulations));
// Set the log variable (will be returned via ref)
log = sb.ToString();
// Return the selected move
return(selected.Move);
}
// Policy to select a move among the children of the given node
// k is the balance between choosing the most successfully simulated
// child nodes vs the most unexplored child nodes
// The higher the k the more weight we put on exploring less explored
// nodes
private TicTacToeMCTSNode SelectMovePolicy(TicTacToeMCTSNode node, float k)
{
float lnN = (float)Math.Log(node.Playouts);
TicTacToeMCTSNode bestChild = null;
float bestUCT = float.NegativeInfinity;
foreach (AbstractMCTSNode <Pos, CellState> childNode in node.Children)
{
float uct = childNode.Wins / (float)childNode.Playouts
+ k * (float)Math.Sqrt(lnN / childNode.Playouts);
if (uct > bestUCT)
{
bestUCT = uct;
bestChild = childNode as TicTacToeMCTSNode;
}
}
return(bestChild);
}
// Run an MCTS iteration
private void MCTS(TicTacToeMCTSNode root)
{
// Current node is the root node
TicTacToeMCTSNode current = root;
// No node is initially selected in the tree policy (selection + expansion)
bool selected = false;
// The move sequence, so we can backpropagate results
Stack <TicTacToeMCTSNode> moveSequence = new Stack <TicTacToeMCTSNode>();
// The root node is the first in the sequence
moveSequence.Push(current);
// Tree policy (selection + expansion), to be performed while the
// current node is not terminal AND no node is selected
// (i.e. the loop stops if the current node becomes terminal OR a
// node is selected)
while (!current.IsTerminal && !selected)
{
// Is the current node fully expanded? (i.e. have we
// tried/expanded all possible moves?)
if (current.IsFullyExpanded)
{
// Then the "new" current node will be selected among the
// children of the "current" current node
current = SelectMovePolicy(current, k);
}
else
{
// Otherwise let's expand one of the currently untried
// moves and select one of its children as the current node
current = ExpandPolicy(current);
selected = true;
}
// Add another node to the sequence
moveSequence.Push(current);
}
// Perform a playout / rollout from the current node until the end
// of the game and obtain the result
CellState result = current.Playout(PlayoutPolicy);
// Backpropagate the result along the move sequence
while (moveSequence.Count > 0)
{
// Pop the top node in the sequence
TicTacToeMCTSNode node = moveSequence.Pop();
// Increment its number of playouts
node.Playouts++;
// Update the win/lose count according whose turn it was to play
// in the previous turn
if (result == node.Turn.Other())
{
node.Wins++;
}
else if (result == node.Turn)
{
node.Wins--;
}
}
}