# What is Monte Carlo tree search?

by Stephen M. Walker II, Co-Founder / CEO

## What is Monte Carlo tree search?

Monte Carlo tree search (MCTS) is an intelligent search algorithm that combines elements of random sampling, simulation, and tree exploration to efficiently explore a large decision space. It has been widely used in games like Go, chess, and poker, as well as other complex domains where traditional search methods may be too slow or computationally expensive.

## How does Monte Carlo tree search work?

The main idea behind MCTS is to iteratively construct a search tree by selecting promising nodes based on their exploration and exploitation potential. This is done through a process called "expand, simulate, backpropagate," which repeats until the desired depth or time limit is reached:

1. Expand — Start from the current node (the root of the tree) and select an unexplored child node to add to the tree. If all children are already expanded, skip this step.

2. Simulate — Perform a random simulation from the newly added child node to the end of the game or episode. This may involve generating random actions or applying heuristics to guide the search process.

3. Backpropagate — Update the statistics for each visited node (e.g., win/loss count and average reward) by propagating the result of the simulation back up the tree.

4. Select — Choose the most promising node among those not yet fully expanded, using an evaluation function that combines exploration and exploitation criteria (e.g., upper confidence bounds applied to trees (UCT)).

The iteration process continues until a stopping condition is met (e.g., maximum depth or time limit). At this point, the algorithm returns the best action found during the search as its final decision.

MCTS has been shown to be highly effective in games with large branching factors and complex evaluation functions, where traditional search methods like minimax or alpha-beta pruning may not perform well due to their exponential growth in computational complexity. By combining random sampling and tree exploration, MCTS can quickly identify promising branches of the decision space while avoiding getting stuck in unpromising areas. This makes it a versatile and efficient tool for tackling various AI challenges across different domains.

## What are the benefits of Monte Carlo tree search?

1. Better exploration: Monte Carlo tree search (MCTS) explores both promising and unpromising branches, allowing the algorithm to better understand the potential outcomes of each move. This can lead to more informed decision-making and improved performance in various applications.
2. Faster convergence: MCTS tends to converge faster than traditional search algorithms like minimax or alpha-beta pruning, especially when dealing with large or complex search spaces. This is because MCTS focuses on the most relevant branches of the tree, ignoring less important ones.
3. Adaptability: MCTS can be easily adapted to different problem domains and search spaces by altering its simulation policy and evaluation function. This makes it a versatile tool for various applications such as game playing, optimization, and planning.
4. Simplicity: MCTS is relatively simple to implement compared to other advanced search algorithms, making it accessible to developers with varying levels of experience. Additionally, the algorithm's parallelizable nature allows for efficient execution on modern computing hardware, further enhancing its performance in real-world applications.

## What are some of the challenges associated with Monte Carlo tree search?

Some of the challenges associated with Monte Carlo tree search include the need for large amounts of computation, difficulty in balancing exploration versus exploitation, and the potential for getting trapped in local optima. Additionally, the algorithm can be sensitive to noise and may not always converge to an optimal solution.

## How can Monte Carlo tree search be used in AI applications?

Monte Carlo tree search (MCTS) can be used in various AI applications where efficient decision-making is required, particularly when dealing with large or complex search spaces. Some examples of MCTS applications include:

1. Game playing — MCTS has been successfully applied to games like Go, chess, and poker, allowing computers to play at a superhuman level by efficiently exploring the vast number of possible moves and evaluating their potential outcomes.

2. Optimization problems — MCTS can be used for solving optimization problems, such as scheduling or resource allocation, by searching for the best possible solution within a given constraint space.

3. Planning and control systems — In robotics or autonomous systems, MCTS can help design effective controllers and planners by allowing agents to explore various strategies and evaluate their performance in simulated environments.

4. Reinforcement learning — MCTS can be combined with reinforcement learning techniques, like Q-learning or policy gradient methods, to improve the efficiency of learning from experience in complex stochastic environments.

5. Combinatorial optimization — MCTS can be used for solving combinatorial optimization problems, such as the traveling salesman problem or vehicle routing problem, by efficiently exploring possible solutions and evaluating their quality based on a given objective function.

By leveraging its strengths in balancing exploration versus exploitation and handling large search spaces, MCTS offers promising opportunities for advancing AI capabilities in various domains.

## More terms

### What is a constrained conditional model?

A Constrained Conditional Model (CCM) is a framework in machine learning that combines the learning of conditional models with declarative constraints within a constrained optimization framework. These constraints can be either hard, which prohibit certain assignments, or soft, which penalize unlikely assignments. The constraints are used to incorporate domain-specific knowledge into the model, allowing for more expressive decision-making in complex output spaces.

### What is R?

R is a programming language and free software environment for statistical computing and graphics supported by the R Foundation for Statistical Computing. The R language is widely used among statisticians and data miners for developing statistical software and data analysis.