DOCSLIB.ORG

Learning to Search with Mctsnets

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Learning to Search with Mctsnets Learning to Search with MCTSnets Arthur Guez * 1 Theophane´ Weber * 1 Ioannis Antonoglou 1 Karen Simonyan 1 Oriol Vinyals 1 Daan Wierstra 1 Remi´ Munos 1 David Silver 1 Abstract is measured, and the backup rule by which those evalua- tions are propagated up the search tree. Our contribution Planning problems are among the most impor- is a new search algorithm in which all of these steps can tant and well-studied problems in artificial intel- be learned automatically and efficiently. Our work fits into ligence. They are most typically solved by tree a more general trend of learning differentiable versions of search algorithms that simulate ahead into the fu- algorithms. ture, evaluate future states, and back-up those eval- uations to the root of a search tree. Among these One particularly powerful and general method for planning algorithms, Monte-Carlo tree search (MCTS) is is Monte-Carlo tree search (MCTS) (Coulom, 2006; Kocsis one of the most general, powerful and widely & Szepesvari´ , 2006), as used in the recent AlphaGo program used. A typical implementation of MCTS uses (Silver et al., 2016). A typical MCTS algorithm consists of cleverly designed rules, optimised to the partic- several phases. First, it simulates trajectories into the future, ular characteristics of the domain. These rules starting from a root state. Second, it evaluates the perfor- control where the simulation traverses, what to mance of leaf states - either using a random rollout, or using evaluate in the states that are reached, and how an evaluation function such as a ’value network’. Third, it to back-up those evaluations. In this paper we backs-up these evaluations to update internal values along instead learn where, what and how to search. Our the trajectory, for example by averaging over evaluations. architecture, which we call an MCTSnet, incorpo- We present a neural network architecture that includes the rates simulation-based search inside a neural net- same processing stages as a typical MCTS, but inside the work, by expanding, evaluating and backing-up neural network itself, as a dynamic computational graph. a vector embedding. The parameters of the net- The key idea is to represent the internal state of the search, work are trained end-to-end using gradient-based at each node, by a memory vector. The computation of optimisation. When applied to small searches the network proceeds forwards from the root state, just like in the well-known planning problem Sokoban, a simulation of MCTS, using a simulation policy based the learned search algorithm significantly outper- on the memory vector to select the trajectory to traverse. formed MCTS baselines. The leaf state is then processed by an embedding network to initialize the memory vector at the leaf. The network proceeds backwards up the trajectory, updating the memory 1. Introduction at each visited state according to a backup network that propagates from child to parent. Finally, the root memory Many success stories in artificial intelligence are based on vector is used to compute an overall prediction of value or arXiv:1802.04697v2 [cs.AI] 17 Jul 2018 the application of powerful tree search algorithms to chal- action. lenging planning problems (Samuel, 1959; Knuth & Moore, 1975;J unger¨ et al., 2009). It has been well documented that The major benefit of our planning architecture, compared planning algorithms can be highly optimised by tailoring to more traditional planning algorithms, is that it can be them to the domain (Schaeffer, 2000). For example, the exposed to gradient-based optimisation. This allows us to performance can often be dramatically improved by modify- replace every component of MCTS with a richer, learnable ing the rules that select the trajectory to traverse, the states equivalent — while maintaining the desirable structural to expand, the evaluation function by which performance properties of MCTS such as the use of a model, iterative local computations, and structured memory. We jointly * 1 Equal contribution DeepMind, London, UK. Correspondence train the parameters of the evaluation network, backup net- to: A. Guez and T. Weber <faguez, [email protected]>. work and simulation policy so as to optimise the overall Proceedings of the 35 th International Conference on Machine predictions of the MCTS network (MCTSnet). The ma- Learning, Stockholm, Sweden, PMLR 80, 2018. Copyright 2018 jority of the network is fully differentiable, allowing for by the author(s). Learning to Search with MCTSnets efficient training by gradient descent. Still, internal action been demonstrated to succeed in any domain approaching sequences directing the control flow of the network cannot the complexity of Sokoban. be differentiated, and learning this internal policy presents a Other neural network architectures have also incorporated challenging credit assignment problem. To address this, we Monte-Carlo simulations. The I2A architecture (Weber propose a novel, generally-applicable approximate scheme et al., 2017) aggregates the results of several simulations into for credit assignment that leverages the anytime property its network computation. MCTSnets both generalise and of our computational graph, allowing us to also effectively extend some ideas behind I2A: introducing a tree structured learn this part of the search network from data. memory that stores node-specific statistics; and learning the In the Sokoban domain, a classic planning task (Botea et al., simulation and tree expansion strategy, rather than rolling 2003), we justify our network design choices and show that out each possible action from the root state with a fixed pol- our learned search algorithm is able to outperform various icy. Similar to I2A, the predictron architecture (Silver et al., model-free and model-based baselines. 2017b) also aggregates over multiple simulations; however, in that case the simulations roll out an implicit transition 2. Related Work model, rather than concrete steps from the actual environ- ment. A recent extension by Farquhar et al.(2017) performs There has been significant previous work on learning evalu- planning over a fixed-tree expansion of such implicit model. ation functions, using supervised learning or reinforcement learning, that are subsequently combined with a search al- 3. MCTSnet gorithm (Tesauro, 1994; Baxter et al., 1998; Silver et al., 2016). However, the learning process is typically decoupled The MCTSnet architecture may be understood from two dis- from the search algorithm, and has no awareness of how tinct but equivalent perspectives. First, it may be understood the search algorithm will combine those evaluations into an as a search algorithm with a control flow that closely mir- overall decision. rors the simulation-based tree traversals of MCTS. Second, it may be understood as a neural network represented by Several previous search architectures have learned to tune a dynamic computation graph that processes input states, the parameters of the evaluation function so as to achieve the performs intermediate computations on hidden states, and most effective overall search results given a specified search outputs a final decision. We present each of these perspec- algorithm. The learning-to-search framework (Chang et al., tives in turn, starting with the original, unmodified search 2015) learns an evaluation function that is effective in the algorithm. context of beam search. Samuel’s checkers player (Samuel, 1959), the TD(leaf) algorithm (Baxter et al., 1998; Schaeffer et al., 2001), and the TreeStrap algorithm apply reinforce- 3.1. MCTS Algorithm ment learning to find an evaluation function that combines The goal of planning is to find the optimal strategy that with minimax search to produce an accurate root evaluation maximises the total reward in an environment defined by a (Veness et al., 2009); while comparison training (Tesauro, deterministic transition model s0 = T (s; a), mapping each 1988) applies supervised learning to the same problem; these state and action to a successor state s0, and a reward model methods have been successful in chess, checkers and shogi. r(s; a), describing the goodness of each transition. In all cases the evaluation function is scalar valued. MCTS is a simulation-based search algorithm that converges There have been a variety of previous efforts to frame the to a solution to the planning problem. At a high level, the learning of internal search decisions as a meta-reasoning idea of MCTS is to maintain statistics at each node, such problem, one which can be optimized directly (Russell, as the visit count and mean evaluation, and to use these 1995). Kocsis et al.(2005) apply black-box optimisation to statistics to decide which branches of the tree to visit. learn the meta-parameters controlling an alpha-beta search, but do not learn fine-grained control over the search deci- MCTS proceeds by running a number of simulations. Each sions. Considering action choices at tree nodes as a bandit simulation traverses the tree, selecting the most promis- problem led to the widely used UCT variant of MCTS (Koc- ing child according to the statistics, until a leaf node is sis & Szepesvari´ , 2006). Hay & Russell(2011) also studied reached. The leaf node is then evaluated using a rollout the meta-problem in MCTS, but they only considered a or value-network (Silver et al., 2016). This value is then myopic policy without function approximation. Pascanu propagated during a back-up phase that updates statistics of et al.(2017) also investigate learning-to-plan using neural the tree along the traversed path, tracking the visit counts networks. However, their system uses an unstructured mem- N(s), N(s; a) and mean evaluation Q(s; a) following from ory which makes complex branching very unlikely. Initial each state s and action a. Search proceeds in an anytime results have been provided for toy domains but it has not yet fashion: the statistics gradually become more accurate, and simulations focus on increasingly promising regions of the Learning to Search with MCTSnets tree.
Load more

Recommended publications
  • Monte-Carlo Tree Search Solver
    Monte-Carlo Tree Search Solver Mark H.M. Winands1, Yngvi BjÄornsson2, and Jahn-Takeshi Saito1 1 Games and AI Group, MICC, Universiteit Maastricht, Maastricht, The Netherlands fm.winands,[email protected] 2 School of Computer Science, Reykjav¶³kUniversity, Reykjav¶³k,Iceland [email protected] Abstract. Recently, Monte-Carlo Tree Search (MCTS) has advanced the ¯eld of computer Go substantially. In this article we investigate the application of MCTS for the game Lines of Action (LOA). A new MCTS variant, called MCTS-Solver, has been designed to play narrow tacti- cal lines better in sudden-death games such as LOA. The variant di®ers from the traditional MCTS in respect to backpropagation and selection strategy. It is able to prove the game-theoretical value of a position given su±cient time. Experiments show that a Monte-Carlo LOA program us- ing MCTS-Solver defeats a program using MCTS by a winning score of 65%. Moreover, MCTS-Solver performs much better than a program using MCTS against several di®erent versions of the world-class ®¯ pro- gram MIA. Thus, MCTS-Solver constitutes genuine progress in using simulation-based search approaches in sudden-death games, signi¯cantly improving upon MCTS-based programs. 1 Introduction For decades ®¯ search has been the standard approach used by programs for playing two-person zero-sum games such as chess and checkers (and many oth- ers). Over the years many search enhancements have been proposed for this framework. However, in some games where it is di±cult to construct an accurate positional evaluation function (e.g., Go) the ®¯ approach was hardly success- ful.
    [Show full text]
  • Αβ-Based Play-Outs in Monte-Carlo Tree Search
    αβ-based Play-outs in Monte-Carlo Tree Search Mark H.M. Winands Yngvi Bjornsson¨ Abstract— Monte-Carlo Tree Search (MCTS) is a recent [9]. In the context of game playing, Monte-Carlo simulations paradigm for game-tree search, which gradually builds a game- were first used as a mechanism for dynamically evaluating tree in a best-first fashion based on the results of randomized the merits of leaf nodes of a traditional αβ-based search [10], simulation play-outs. The performance of such an approach is highly dependent on both the total number of simulation play- [11], [12], but under the new paradigm MCTS has evolved outs and their quality. The two metrics are, however, typically into a full-fledged best-first search procedure that replaces inversely correlated — improving the quality of the play- traditional αβ-based search altogether. MCTS has in the past outs generally involves adding knowledge that requires extra couple of years substantially advanced the state-of-the-art computation, thus allowing fewer play-outs to be performed in several game domains where αβ-based search has had per time unit. The general practice in MCTS seems to be more towards using relatively knowledge-light play-out strategies for difficulties, in particular computer Go, but other domains the benefit of getting additional simulations done. include General Game Playing [13], Amazons [14] and Hex In this paper we show, for the game Lines of Action (LOA), [15]. that this is not necessarily the best strategy. The newest version The right tradeoff between search and knowledge equally of our simulation-based LOA program, MC-LOAαβ , uses a applies to MCTS.
    [Show full text]
  • Smartk: Efficient, Scalable and Winning Parallel MCTS
    SmartK: Efficient, Scalable and Winning Parallel MCTS Michael S. Davinroy, Shawn Pan, Bryce Wiedenbeck, and Tia Newhall Swarthmore College, Swarthmore, PA 19081 ACM Reference Format: processes. Each process constructs a distinct search tree in Michael S. Davinroy, Shawn Pan, Bryce Wiedenbeck, and Tia parallel, communicating only its best solutions at the end of Newhall. 2019. SmartK: Efficient, Scalable and Winning Parallel a number of rollouts to pick a next action. This approach has MCTS. In SC ’19, November 17–22, 2019, Denver, CO. ACM, low communication overhead, but significant duplication of New York, NY, USA, 3 pages. https://doi.org/10.1145/nnnnnnn.nnnnnnneffort across processes. 1 INTRODUCTION Like root parallelization, our SmartK algorithm achieves low communication overhead by assigning independent MCTS Monte Carlo Tree Search (MCTS) is a popular algorithm tasks to processes. However, SmartK dramatically reduces for game playing that has also been applied to problems as search duplication by starting the parallel searches from many diverse as auction bidding [5], program analysis [9], neural different nodes of the search tree. Its key idea is it uses nodes’ network architecture search [16], and radiation therapy de- weights in the selection phase to determine the number of sign [6]. All of these domains exhibit combinatorial search processes (the amount of computation) to allocate to ex- spaces where even moderate-sized problems can easily ex- ploring a node, directing more computational effort to more haust computational resources, motivating the need for par- promising searches. allel approaches. SmartK is our novel parallel MCTS algo- Our experiments with an MPI implementation of SmartK rithm that achieves high performance on large clusters, by for playing Hex show that SmartK has a better win rate and adaptively partitioning the search space to efficiently utilize scales better than other parallelization approaches.
    [Show full text]
  • Monte-Carlo Tree Search
    Monte-Carlo Tree Search PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit Maastricht, op gezag van de Rector Magnificus, Prof. mr. G.P.M.F. Mols, volgens het besluit van het College van Decanen, in het openbaar te verdedigen op donderdag 30 september 2010 om 14:00 uur door Guillaume Maurice Jean-Bernard Chaslot Promotor: Prof. dr. G. Weiss Copromotor: Dr. M.H.M. Winands Dr. B. Bouzy (Universit´e Paris Descartes) Dr. ir. J.W.H.M. Uiterwijk Leden van de beoordelingscommissie: Prof. dr. ir. R.L.M. Peeters (voorzitter) Prof. dr. M. Muller¨ (University of Alberta) Prof. dr. H.J.M. Peters Prof. dr. ir. J.A. La Poutr´e (Universiteit Utrecht) Prof. dr. ir. J.C. Scholtes The research has been funded by the Netherlands Organisation for Scientific Research (NWO), in the framework of the project Go for Go, grant number 612.066.409. Dissertation Series No. 2010-41 The research reported in this thesis has been carried out under the auspices of SIKS, the Dutch Research School for Information and Knowledge Systems. ISBN 978-90-8559-099-6 Printed by Optima Grafische Communicatie, Rotterdam. Cover design and layout finalization by Steven de Jong, Maastricht. c 2010 G.M.J-B. Chaslot. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronically, mechanically, photocopying, recording or otherwise, without prior permission of the author. Preface When I learnt the game of Go, I was intrigued by the contrast between the simplicity of its rules and the difficulty to build a strong Go program.
    [Show full text]
  • CS234 Notes - Lecture 14 Model Based RL, Monte-Carlo Tree Search
    CS234 Notes - Lecture 14 Model Based RL, Monte-Carlo Tree Search Anchit Gupta, Emma Brunskill June 14, 2018 1 Introduction In this lecture we will learn about model based RL and simulation based tree search methods. So far we have seen methods which attempt to learn either a value function or a policy from experience. In contrast model based approaches first learn a model of the world from experience and then use this for planning and acting. Model-based approaches have been shown to have better sample efficiency and faster convergence in certain settings. We will also have a look at MCTS and its variants which can be used for planning given a model. MCTS was one of the main ideas behind the success of AlphaGo. Figure 1: Relationships among learning, planning, and acting 2 Model Learning By model we mean a representation of an MDP < S; A; R; T; γ> parametrized by η. In the model learning regime we assume that the state and action space S; A are known and typically we also assume conditional independence between state transitions and rewards i.e P [st+1; rt+1jst; at] = P [st+1jst; at]P [rt+1jst; at] Hence learning a model consists of two main parts the reward function R(:js; a) and the transition distribution P (:js; a). k k k k K Given a set of real trajectories fSt ;At Rt ; :::; ST gk=1 model learning can be posed as a supervised learning problem. Learning the reward function R(s; a) is a regression problem whereas learning the transition function P (s0js; a) is a density estimation problem.
    [Show full text]
  • An Analysis of Monte Carlo Tree Search
    Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17) An Analysis of Monte Carlo Tree Search Steven James,∗ George Konidaris,† Benjamin Rosman∗‡ ∗University of the Witwatersrand, Johannesburg, South Africa †Brown University, Providence RI 02912, USA ‡Council for Scientific and Industrial Research, Pretoria, South Africa [email protected], [email protected], [email protected] Abstract UCT calls for rollouts to be performed by randomly se- lecting actions until a terminal state is reached. The outcome Monte Carlo Tree Search (MCTS) is a family of directed of the simulation is then propagated to the root of the tree. search algorithms that has gained widespread attention in re- cent years. Despite the vast amount of research into MCTS, Averaging these results over many iterations performs re- the effect of modifications on the algorithm, as well as the markably well, despite the fact that actions during the sim- manner in which it performs in various domains, is still not ulation are executed completely at random. As the outcome yet fully known. In particular, the effect of using knowledge- of the simulations directly affects the entire algorithm, one heavy rollouts in MCTS still remains poorly understood, with might expect that the manner in which they are performed surprising results demonstrating that better-informed rollouts has a major effect on the overall strength of the algorithm. often result in worse-performing agents. We present exper- A natural assumption to make is that completely random imental evidence suggesting that, under certain smoothness simulations are not ideal, since they do not map to realistic conditions, uniformly random simulation policies preserve actions.
    [Show full text]
  • CS 188: Artificial Intelligence Game Playing State-Of-The-Art
    CS 188: Artificial Intelligence Game Playing State-of-the-Art § Checkers: 1950: First computer player. 1994: First Adversarial Search computer champion: Chinook ended 40-year-reign of human champion Marion Tinsley using complete 8-piece endgame. 2007: Checkers solved! § Chess: 1997: Deep Blue defeats human champion Gary Kasparov in a six-game match. Deep Blue examined 200M positions per second, used very sophisticated evaluation and undisclosed methods for extending some lines of search up to 40 ply. Current programs are even better, if less historic. § Go: Human champions are now starting to be challenged by machines. In go, b > 300! Classic programs use pattern knowledge bases, but big recent advances use Monte Carlo (randomized) expansion methods. Instructors: Pieter Abbeel & Dan Klein University of California, Berkeley [These slides were created by Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC Berkeley (ai.berkeley.edu).] Game Playing State-of-the-Art Behavior from Computation § Checkers: 1950: First computer player. 1994: First computer champion: Chinook ended 40-year-reign of human champion Marion Tinsley using complete 8-piece endgame. 2007: Checkers solved! § Chess: 1997: Deep Blue defeats human champion Gary Kasparov in a six-game match. Deep Blue examined 200M positions per second, used very sophisticated evaluation and undisclosed methods for extending some lines of search up to 40 ply. Current programs are even better, if less historic. § Go: 2016: Alpha GO defeats human champion. Uses Monte Carlo Tree Search, learned
    [Show full text]
  • A Survey of Monte Carlo Tree Search Methods
    IEEE TRANSACTIONS ON COMPUTATIONAL INTELLIGENCE AND AI IN GAMES, VOL. 4, NO. 1, MARCH 2012 1 A Survey of Monte Carlo Tree Search Methods Cameron Browne, Member, IEEE, Edward Powley, Member, IEEE, Daniel Whitehouse, Member, IEEE, Simon Lucas, Senior Member, IEEE, Peter I. Cowling, Member, IEEE, Philipp Rohlfshagen, Stephen Tavener, Diego Perez, Spyridon Samothrakis and Simon Colton Abstract—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 summarise the results from the key game and non-game domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work. Index Terms—Monte Carlo Tree Search (MCTS), Upper Confidence Bounds (UCB), Upper Confidence Bounds for Trees (UCT), Bandit-based methods, Artificial Intelligence (AI), Game search, Computer Go. F 1 INTRODUCTION ONTE Carlo Tree Search (MCTS) is a method for M finding optimal decisions in a given domain by taking random samples in the decision space and build- ing a search tree according to the results. It has already had a profound impact on Artificial Intelligence (AI) approaches for domains that can be represented as trees of sequential decisions, particularly games and planning problems.
    [Show full text]
  • Monte Carlo *-Minimax Search
    Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Monte Carlo *-Minimax Search Marc Lanctot Abdallah Saffidine Department of Knowledge Engineering LAMSADE, Maastricht University, Netherlands Universite´ Paris-Dauphine, France [email protected] abdallah.saffi[email protected] Joel Veness and Christopher Archibald, Mark H. M. Winands Department of Computing Science Department of Knowledge Engineering University of Alberta, Canada Maastricht University, Netherlands fveness@cs., [email protected] [email protected] Abstract the search enhancements from the classic αβ literature can- not be easily adapted to MCTS. The classic algorithms for This paper introduces Monte Carlo *-Minimax stochastic games, EXPECTIMAX and *-Minimax (Star1 and Search (MCMS), a Monte Carlo search algorithm Star2), perform look-ahead searches to a limited depth. How- for turned-based, stochastic, two-player, zero-sum ever, the running time of these algorithms scales exponen- games of perfect information. The algorithm is de- tially in the branching factor at chance nodes as the search signed for the class of densely stochastic games; horizon is increased. Hence, their performance in large games that is, games where one would rarely expect to often depends heavily on the quality of the heuristic evalua- sample the same successor state multiple times at tion function, as only shallow searches are possible. any particular chance node. Our approach com- bines sparse sampling techniques from MDP plan- One way to handle the uncertainty at chance nodes would ning with classic pruning techniques developed for be forward pruning [Smith and Nau, 1993], but the perfor- adversarial expectimax planning. We compare and mance gain until now has been small [Schadd et al., 2009].
    [Show full text]
  • Using Monte Carlo Tree Search As a Demonstrator Within Asynchronous Deep RL
    Using Monte Carlo Tree Search as a Demonstrator within Asynchronous Deep RL Bilal Kartal∗, Pablo Hernandez-Leal∗ and Matthew E. Taylor fbilal.kartal,pablo.hernandez,[email protected] Borealis AI, Edmonton, Canada Abstract There are several ways to get the best of both DRL and search methods. For example, AlphaGo Zero (Silver et al. Deep reinforcement learning (DRL) has achieved great suc- 2017) and Expert Iteration (Anthony, Tian, and Barber 2017) cesses in recent years with the help of novel methods and concurrently proposed the idea of combining DRL and higher compute power. However, there are still several chal- MCTS in an imitation learning framework where both com- lenges to be addressed such as convergence to locally opti- mal policies and long training times. In this paper, firstly, ponents improve each other. These works combine search we augment Asynchronous Advantage Actor-Critic (A3C) and neural networks sequentially. First, search is used to method with a novel self-supervised auxiliary task, i.e. Ter- generate an expert move dataset which is used to train a pol- minal Prediction, measuring temporal closeness to terminal icy network (Guo et al. 2014). Second, this network is used states, namely A3C-TP. Secondly, we propose a new frame- to improve expert search quality (Anthony, Tian, and Barber work where planning algorithms such as Monte Carlo tree 2017), and this is repeated in a loop. However, expert move search or other sources of (simulated) demonstrators can be data collection by vanilla search algorithms can be slow in a integrated to asynchronous distributed DRL methods. Com- sequential framework (Guo et al.
    [Show full text]
  • Comparission Study of MCTS Versus Alpha-Beta Methods
    Charles University in Prague Faculty of Mathematics and Physics BACHELOR THESIS Tom´aˇsJakl Arimaa challenge – comparission study of MCTS versus alpha-beta methods Department of Theoretical Computer Science and Mathematical Logic Supervisor of the bachelor thesis: Mgr. Vladan Majerech, Dr. Study programme: Computer Science Specialization: General Computer Science Prague 2011 I would like to thank to my family for their support, and to Jakub Slav´ık and Jan Vanˇeˇcek for letting me stay in their flat at the end of the work. I would also like to thank to my supervisor for very useful and relevant comments he gave me. I declare that I carried out this bachelor thesis independently, and only with the cited sources, literature and other professional sources. I understand that my work relates to the rights and obligations under the Act No. 121/2000 Coll., the Copyright Act, as amended, in particular the fact that the Charles University in Prague has the right to conclude a license agreement on the use of this work as a school work pursuant to Section 60 paragraph 1 of the Copyright Act. In Prague date August 5, 2011 Tom´aˇsJakl Title: Arimaa challenge – comparission study of MCTS versus alpha-beta methods Author: Tom´aˇsJakl Department: Department of Theoretical Computer Science and Mathematical Logic Supervisor: Mgr. Vladan Majerech, Dr., Department of Theoretical Computer Science and Mathematical Logic Abstract: In the world of chess programming the most successful algorithm for game tree search is considered AlphaBeta search, however in game of Go it is Monte Carlo Tree Search. The game of Arimaa has similarities with both Go and Chess, but there has been no successful program using Monte Carlo Tree Search so far.
    [Show full text]
  • The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions
    The Grand Challenge of Computer Go: Monte Carlo Tree Search and Extensions Sylvain Gelly*, EPC TAO, INRIA Saclay & LRI Marc Schoenauer, Bât. 490, Université Paris-Sud Michèle Sebag, 91405 Orsay Cedex, France Olivier Teytaud *Now in Google Zurich Levente Kocsis David Silver Csaba Szepesvári MTA SZTAKI University College London University of Alberta Kende u. 13–17. Dept. of Computer Science Dept. of Computing Science Budapest 1111, Hungary London, WC1E 6BT, UK Edmonton T6G 2E8, Canada ABSTRACT Go. The size of the search space in Go is so large that it The ancient oriental game of Go has long been considered a defies brute force search. Furthermore, it is hard to charac- grand challenge for artificial intelligence. For decades, com- terize the strength of a position or move. For these reasons, puter Go has defied the classical methods in game tree search Go remains a grand challenge of artificial intelligence; the that worked so successfully for chess and checkers. How- field awaits a triumph analogous to the 1997 chess match in ever, recent play in computer Go has been transformed by a which Deep Blue defeated the world champion Gary Kas- new paradigm for tree search based on Monte-Carlo meth- parov [22]. ods. Programs based on Monte-Carlo tree search now play The last five years have witnessed considerable progress in at human-master levels and are beginning to challenge top computer Go. With the development of new Monte-Carlo professional players. In this paper we describe the leading algorithms for tree search [12, 18], computer Go programs algorithms for Monte-Carlo tree search and explain how they have achieved some remarkable successes [15, 12], including have advanced the state of the art in computer Go.
    [Show full text]