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

GAMES: A new Scenario for Software and Knowledge Reuse

Games are a well-known test bed for testing search algorithms and learning methods, and many authors have presented numerous reasons for the research in this area. Nevertheless, they have not received the attention they deserve as software projects. In this paper, we analyze the applicability of software and knowledge reuse in the games domain. In spite of the need to find a good evaluation function, search algorithms and interface design can be said to be the primary concerns. In addition, we will discuss the current state of the main statistical learning methods and how they can be addressed from a software engineering point of view. So, this paper proposes a reliable environment and adequate tools, necessary in order to achieve high levels of reuse in the games domain

An exponential lower bound for Individualization-Refinement algorithms for Graph Isomorphism

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in practice, from a theoretical point of view, no general lower bounds concerning the worst case complexity of these tools are known. In fact, it is an open question whether individualization-refinement algorithms can achieve upper bounds on the running time similar to the more theoretical techniques based on a group theoretic approach. In this work we give a negative answer to this question and construct a family of graphs on which algorithms based on the individualization-refinement paradigm require exponential time. Contrary to a previous construction of Miyazaki, that only applies to a specific implementation within the individualization-refinement framework, our construction is immune to changing the cell selector, or adding various heuristic invariants to the algorithm. Furthermore, our graphs also provide exponential lower bounds in the case when the $k$-dimensional Weisfeiler-Leman algorithm is used to replace the standard color refinement operator and the arguments even work when the entire automorphism group of the inputs is initially provided to the algorithm.Comment: 21 page