Monte Carlo Tree Search (MCTS) is a decision-making algorithm widely used in Reinforcement Learning for games, robotics and other applications. The algorithm employs a tree representation of the game or problem state space, and simulates random gameplays from the current state to reach an optimal action while providing confidence values for the outcomes. MCTS has been successful in many domains, including the popular AlphaGo computer program that defeated the world champion Go player.
Generally, MCTS consists of four distinct stages – selection, expansion, simulation, and back-propagation. Here is a step-by-step explanation of how MCTS works in the context of a Reinforcement Learning problem:
1. Selection: Starting from the current state, MCTS selects node(s) to expand further in the search tree based on a predefined traversal policy. This policy balances between exploitation and exploration to balance the trade-off between selecting the best known move and exploring new moves. Generally, UCT (Upper Confidence Bounds applied to Trees) policy, which is a variation of Thompson sampling and takes into account both exploration and exploitation, is used.
2. Expansion: After selecting the node(s), MCTS expands the search tree to add new leaves. These are nodes that are not yet visited during the previous iterations of MCTS.
3. Simulation: Once the search tree is expanded, MCTS simulates random gameplays rolling out from the newly created leaves until a terminal state is reached. The simulation ends when a maximum depth or a timeout is reached.
4. Back-propagation: In this final step, the simulator evaluates the outcome of the random rollouts, and the values are propagated upwards through the tree. The visit count and simulation outcomes of each node in the visited path are updated based on the rollout outcome.
The final result of the MCTS algorithm is the root node, which is an action to take in the current game or problem state.
The MCTS algorithm can be used to search large state spaces in Reinforcement Learning applications. For instance, in a Chess game, the branching factor of the game tree is enormous and non-uniform: each player has up to 20 legal moves at their disposal in a given state. With 5 ply, the complexity of expanded nodes is above 3 million nodes. MCTS algorithm adapts to such a large space by only expanding states that have high potential of winning the game; the tree itself ’grows’ as MCTS is performed, so it becomes more likely to reach a winning strategy over time. It is robust and scalable as the algorithm is independent of the problem domain and is effective in cases where heuristics are not appropriate, and the domain is too vast to explore entirely.
In conclusion, Monte Carlo Tree Search (MCTS) is an effective decision-making algorithm in Reinforcement Learning, and can handle the high-complexity of large state spaces that are common in many applications.