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MCTS was initially developed for playing board games, such as Go, where the number of possible moves grows exponentially with each turn. However, it has been successfully adapted to various other domains, including video games, robotics, and optimization problems.
The key idea behind MCTS is to perform a guided random search in the game tree, focusing more on promising branches and avoiding wasteful exploration. The algorithm builds and maintains a tree structure, where each node represents a state in the game and holds essential statistics for guiding the search process.
The core steps of the Monte Carlo Tree Search algorithm are as follows:
- Selection: Starting from the root node, the algorithm navigates through the tree using a selection policy to find the most promising node based on some evaluation criteria. Typically, the Upper Confidence Bound for Trees (UCT) formula is used for selection. It balances between exploring less visited nodes and exploiting nodes that seem to have higher potential.
- Expansion: Once the selection reaches a node that is not fully expanded (i.e., it doesn't have all possible child nodes), the algorithm expands the tree by adding one or more child nodes representing possible moves from the current state.
- Simulation (Rollout): The MCTS algorithm performs a random playout from the newly expanded node. This random simulation continues until a terminal state is reached. The result of the simulation is a reward (or score) indicating the outcome of the game, which can be a win, loss, or draw.
- Backpropagation: After the simulation, the algorithm backpropagates the reward from the terminal node back up the tree to update the statistics of the nodes along the path taken in the Selection phase. This information helps to adjust the evaluation and selection policies for future iterations.
These four steps are repeatedly performed in a loop, allowing the MCTS algorithm to iteratively improve its understanding of the game's state space. Over time, the algorithm converges towards making better-informed decisions, as it allocates more simulations to the most promising branches of the tree.
MCTS has proven to be highly effective in many applications and has achieved significant breakthroughs in playing complex games like Go and Chess. Its ability to handle vast search spaces and perform well with limited domain knowledge makes it a popular choice for developing intelligent agents in various domains.