A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Monte Carlo Tree Search with Heuristic Evaluations using Implicit Minimax Backups

Monte Carlo Tree Search (MCTS) has improved the performance of game engines in domains such as Go, Hex, and general game playing. MCTS has been shown to outperform classic alpha-beta search in games where good heuristic evaluations are difficult to obtain. In recent years, combining ideas from traditional minimax search in MCTS has been shown to be advantageous in some domains, such as Lines of Action, Amazons, and Breakthrough. In this paper, we propose a new way to use heuristic evaluations to guide the MCTS search by storing the two sources of information, estimated win rates and heuristic evaluations, separately. Rather than using the heuristic evaluations to replace the playouts, our technique backs them up implicitly during the MCTS simulations. These minimax values are then used to guide future simulations. We show that using implicit minimax backups leads to stronger play performance in Kalah, Breakthrough, and Lines of Action.Comment: 24 pages, 7 figures, 9 tables, expanded version of paper presented at IEEE Conference on Computational Intelligence and Games (CIG) 2014 conferenc

Generalized Nested Rollout Policy Adaptation with Limited Repetitions

Generalized Nested Rollout Policy Adaptation (GNRPA) is a Monte Carlo search algorithm for optimizing a sequence of choices. We propose to improve on GNRPA by avoiding too deterministic policies that find again and again the same sequence of choices. We do so by limiting the number of repetitions of the best sequence found at a given level. Experiments show that it improves the algorithm for three different combinatorial problems: Inverse RNA Folding, the Traveling Salesman Problem with Time Windows and the Weak Schur problem

On monte carlo tree search and reinforcement learning

Fuelled by successes in Computer Go, Monte Carlo tree search (MCTS) has achieved widespread adoption within the games community. Its links to traditional reinforcement learning (RL) methods have been outlined in the past; however, the use of RL techniques within tree search has not been thoroughly studied yet. In this paper we re-examine in depth this close relation between the two fields; our goal is to improve the cross-awareness between the two communities. We show that a straightforward adaptation of RL semantics within tree search can lead to a wealth of new algorithms, for which the traditional MCTS is only one of the variants. We confirm that planning methods inspired by RL in conjunction with online search demonstrate encouraging results on several classic board games and in arcade video game competitions, where our algorithm recently ranked first. Our study promotes a unified view of learning, planning, and search

General Board Game Concepts

Many games often share common ideas or aspects between them, such as their rules, controls, or playing area. However, in the context of General Game Playing (GGP) for board games, this area remains under-explored. We propose to formalise the notion of "game concept", inspired by terms generally used by game players and designers. Through the Ludii General Game System, we describe concepts for several levels of abstraction, such as the game itself, the moves played, or the states reached. This new GGP feature associated with the ludeme representation of games opens many new lines of research. The creation of a hyper-agent selector, the transfer of AI learning between games, or explaining AI techniques using game terms, can all be facilitated by the use of game concepts. Other applications which can benefit from game concepts are also discussed, such as the generation of plausible reconstructed rules for incomplete ancient games, or the implementation of a board game recommender system

Learning Policies from Self-Play with Policy Gradients and MCTS Value Estimates

In recent years, state-of-the-art game-playing agents often involve policies that are trained in self-playing processes where Monte Carlo tree search (MCTS) algorithms and trained policies iteratively improve each other. The strongest results have been obtained when policies are trained to mimic the search behaviour of MCTS by minimising a cross-entropy loss. Because MCTS, by design, includes an element of exploration, policies trained in this manner are also likely to exhibit a similar extent of exploration. In this paper, we are interested in learning policies for a project with future goals including the extraction of interpretable strategies, rather than state-of-the-art game-playing performance. For these goals, we argue that such an extent of exploration is undesirable, and we propose a novel objective function for training policies that are not exploratory. We derive a policy gradient expression for maximising this objective function, which can be estimated using MCTS value estimates, rather than MCTS visit counts. We empirically evaluate various properties of resulting policies, in a variety of board games.Comment: Accepted at the IEEE Conference on Games (CoG) 201

Guiding Monte Carlo tree searches with neural networks in the game of go

A dissertation submitted in fulfillment of the requirements to the degree of Master in Computer Science and Computer EngineeringO jogo de tabuleiro Go é um dos poucos jogos determinísticos em que os computadores ainda não conseguem vencer jogadores humanos profissionais consistentemente. Neste trabalho dois métodos de aprendizagem – por um algoritmo genético e por treino por propagação do erro – são utilizados para criar redes neuronais capazes de assistir um algoritmo de pesquisa em árvore de Monte Carlo. Este último algoritmo tem sido o mais bem sucedido na última década de investigação sobre Go. A utilização de uma rede neuronal é uma abordagem que está a sofrer uma revitalização, com os recentes sucessos de redes neuronais profundas de convolução. Estas necessitam, contudo, de recursos que ainda são muitas vezes proibitivos. Este trabalho explora o impacto de redes neuronais mais simples e a produção de um software representativo do estado da arte. Para isto é complementado com técnicas para pesquisas em árvore de Monte Carlo, aquisição automática de conhecimento, paralelismo em árvore, otimização e outros problemas presentes na computação aplicada ao jogo de Go. O software produzido – Matilda – é por isso o culminar de um conjunto de experiências nesta área.Abstract: The game of Go remains one of the few deterministic perfect information games where computer players still struggle against professional human players. In this work two methods of derivation of artificial neural networks – by genetic evolution of symbiotic populations, and by training of multilayer perceptron networks with backpropagation – are analyzed for the production of a neural network suitable for guiding a Monte Carlo tree search algorithm. This last family of algorithms has been the most successful in computer Go software in the last decade. Using a neural network to reduce the branching complexity of the search is an approach to the problema that is currently being revitalized, with the advent of the application of deep convolution neural networks. DCNN however require computational facilities that many computers still don’t have. This work explores the impact of simpler neural networks for the purpose of guiding Monte Carlo tree searches, and the production of a state-of-the-art computer Go program. For this several improvements to Monte Carlo tree searches are also explored. The work is further built upon with considerations related to the parallelization of the search, and the addition of other componentes necessary for competitive programs such as time control mechanisms and opening books. Time considerations for playing against humans are also proposed for na extra psychological advantage. The final software – named Matilda– is not only the sum of a series of experimental parts surrounding Monte Carlo Tree Search applied to Go, but also an attempt at the strongest possible solution for shared memory systems

Structured parallel programming for Monte Carlo Tree Search

The thesis is part of a bigger project, the HEPGAME (High Energy Physics Game). The main objective for HEPGAME is the utilization of AI solutions, particularly by using MCTS for simplification of HEP calculations. One of the issues is solving mathematical expressions of interest with millions of terms. These calculations can be solved with the FORM program, which is software for symbolic manipulation. Since these calculations are computationally intensive and take a large amount of time, the FORM program was parallelized to solve them in a reasonable amount of time.Therefore, any new algorithm based on MCTS, should also be parallelized. This requirement was behind the problem statement of the thesis: “How do we design a structured pattern-based parallel programming approach for efficient parallelism of MCTS for both multi-core and manycore shared-memory machines?”.To answer this question, the thesis approached the MCTS parallelization problem in three levels: (1) implementation level, (2) data structure level, and (3) algorithm level.In the implementation level, we proposed task-level parallelization over thread-level parallelization. Task-level parallelization provides us with efficient parallelism for MCTS to utilize cores on both multi-core and manycore machines.In the data structure level, we presented a lock-free data structure that guarantees the correctness. A lock-free data structure (1) removes the synchronization overhead when a parallel program needs many tasks to feed its cores and (2) improves both performance and scalability.In the algorithm level, we first explained how to use pipeline pattern for parallelization of MCTS to overcome search overhead. Then, through a step by step approach, we were able to propose and detail the structured parallel programming approach for Monte Carlo Tree Search.Algorithms and the Foundations of Software technolog