DOCSLIB.ORG

Monte Carlo Tree Search for Games with Hidden Information and Uncertainty

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Monte Carlo Tree Search for Games with Hidden Information and Uncertainty Monte Carlo Tree Search for games with Hidden Information and Uncertainty Daniel Whitehouse PhD University of York Computer Science August, 2014 Abstract Monte Carlo Tree Search (MCTS) is an AI technique that has been success- fully applied to many deterministic games of perfect information, leading to large advances in a number of domains, such as Go and General Game Play- ing. Imperfect information games are less well studied in the field of AI despite being popular and of significant commercial interest, for example in the case of computer and mobile adaptations of turn based board and card games. This is largely because hidden information and uncertainty leads to a large increase in complexity compared to perfect information games. In this thesis MCTS is extended to games with hidden information and un- certainty through the introduction of the Information Set MCTS (ISMCTS) family of algorithms. It is demonstrated that ISMCTS can handle hidden in- formation and uncertainty in a variety of complex board and card games. This is achieved whilst preserving the general applicability of MCTS and using com- putational budgets appropriate for use in a commercial game. The ISMCTS algorithm is shown to outperform the existing approach of Perfect Information Monte Carlo (PIMC) search. Additionally it is shown that ISMCTS can be used to solve two known issues with PIMC search, namely strategy fusion and non-locality. ISMCTS has been integrated into a commercial game, Spades by AI Factory, with over 2:5 million downloads. The Information Capture And ReUSe (ICARUS) framework is also intro- duced in this thesis. The ICARUS framework generalises MCTS enhancements in terms of information capture (from MCTS simulations) and reuse (to improve MCTS tree and simulation policies). The ICARUS framework is used to express existing enhancements, to provide a tool to design new ones, and to rigorously define how MCTS enhancements can be combined. The ICARUS framework is tested across a wide variety of games. Contents Abstract . .i Contents . ii List of Figures . .v List of Tables . vii List of Algorithms . viii Preface . ix Acknowledgements . xi Author's Declaration . xii 1 Introduction 1 1.1 Background . .3 1.1.1 Monte Carlo Tree Search . .5 1.2 UCT for Games and Beyond . .6 1.3 Research Hypothesis and Project Outcomes . .7 1.3.1 Additional Project Outcomes . .8 1.4 Thesis Overview . 11 2 Notation and Definitions 13 2.1 Games with Hidden Information and Uncertainty . 13 2.2 Game Notation . 16 2.3 Solution concepts for games . 20 2.4 Statistical Analysis of Experiments . 21 3 Literature Review 22 3.1 Multi-Armed Bandits . 22 3.1.1 k-Armed Multi-Armed Bandit Problem . 23 3.1.2 Bandit Algorithms . 23 3.2 Monte Carlo Tree Search . 24 3.2.1 Monte Carlo Tree Search Algorithms . 24 3.2.2 Properties of Monte Carlo Tree Search . 25 3.2.3 Enhancements and Applications . 26 3.2.4 Simultaneous Moves . 27 3.2.5 Multiplayer Games . 29 3.3 Search in Imperfect Information Games . 29 3.3.1 Determinization . 29 ii 3.3.2 Minimax . 31 3.3.3 Monte Carlo Tree Search . 32 3.3.4 Counterfactual Regret Minimization . 32 3.3.5 Inference . 33 4 Software and Domains 34 4.1 MctsFramework . 34 4.1.1 Components of MctsFramework . 35 4.1.2 Handling Hidden Information . 36 4.1.3 Card Games Framework . 36 4.1.4 Integration with BOINC . 37 4.2 Domains . 37 4.2.1 Dou Di Zhu . 37 4.2.2 Mini Dou Di Zhu . 39 4.2.3 Hearts . 40 4.2.4 Spades . 41 4.2.5 Lord of the Rings: The Confrontation . 42 4.2.6 Rules . 43 4.2.7 Phantom m; n; k-games . 45 4.2.8 Checkers . 46 4.2.9 Othello . 46 4.2.10 Backgammon . 47 4.2.11 The Resistance . 47 4.2.12 Scotland Yard . 48 4.2.13 Saboteur . 49 4.2.14 Other Implemented games . 50 5 Hidden Information and Strategy Fusion 51 5.1 Perfect Information Monte Carlo Search . 53 5.1.1 Balancing Simulations and Determinizations . 54 5.1.2 Quantifying the effect of strategy fusion and non-locality 61 5.2 Information Set Monte Carlo Tree Search (ISMCTS) . 67 5.2.1 Subset-armed Bandits . 68 5.2.2 Handling Chance Events . 70 5.2.3 The ISMCTS Algorithm . 71 5.2.4 Evaluating ISMCTS . 76 5.3 Summary . 83 6 Partial Observability 88 6.1 ISMCTS and Partial Observability . 90 6.2 Bandit algorithms for Simultaneous Actions . 91 6.3 ISMCTS with Partially Observable Moves . 92 6.3.1 Algorithms . 92 6.3.2 Experiments . 95 6.4 Summary . 106 iii 7 Bluffing and Inference 111 7.1 Background . 113 7.1.1 Existing Approaches . 114 7.2 ISMCTS with multiple opponent trees . 116 7.3 Inference using MCTS statistics . 118 7.4 Self-determinization and bluffing . 120 7.5 Experiments . 123 7.5.1 Inference and self-determinization methods for The Resis- tance . 123 7.5.2 Balancing true and self-determinizations . 124 7.5.3 Emergence of bluffing . 125 7.5.4 Effect of inference on the belief distribution . 127 7.5.5 Application to other games . 129 7.6 Summary . 132 8 Information Capture and Reuse (ICARUS) 134 8.1 Motivation . 135 8.2 Information Capture And ReUse Strategies (ICARUSes) . 137 8.2.1 Defining ICARUSes . 137 8.2.2 Baseline ICARUS definition . 141 8.2.3 Enhancements in the ICARUS framework . 141 8.2.4 Combining ICARUSes . 148 8.2.5 Convergence properties of ICARUSes . 149 8.3 Episodic Information Capture and Reuse . 151 8.3.1 Definition of EPIC . 152 8.3.2 Episode functions for experimental domains . 154 8.4 Comparing ICARUSes . 156 8.5 Experiments . 159 8.5.1 Strength of ICARUS combinations . 159 8.5.2 EPIC compared to NAST . 165 8.5.3 Simulation policies for MAST . 165 8.5.4 N-gram lengths . 168 8.5.5 Computation time . 171 8.6 Summary . 172 9 Conclusion 175 9.1 Remarks on the Effectiveness of ISMCTS . 178 9.2 Future Work . 180 Bibliography 182 iv List of Figures 5.1 Histogram of win rates for the landlord player in 100 sets of 1000 Dou Di Zhu games. 56 5.2 Plot of number of landlord (player 1) wins against number of determinizations, for fixed numbers of UCT iterations per deter- minization. 58 5.3 Plot of number of landlord (player 1) wins against number of UCT iterations per determinization, for fixed numbers of deter- minizations. 58 5.4 Plot of number of landlord (player 1) wins against number of determinizations, for a fixed number of UCT simulations divided equally among all determinizations. 59 5.5 Results of the determinization balancing experiment for LOTR:C. 60 5.6 Illustration of search trees for (a) determinization and (b) infor- mation set expectimax. 64 5.7 Performance of several agents in Mini Dou Di Zhu. 66 5.8 An example game tree for a simple 1-player game. 73 5.9 An information set search tree for the game shown in Figure 5.8. 73 5.10 An example game tree for a simple 2-player game. 74 5.11 An information set search tree for the game shown in Figure 5.10. 74 5.12 Playing strength of ISMCTS and Determinized UCT for Dou Di Zhu. .................................. 80 5.13 Playing strengths of ISMCTS and PIMC (Determinized UCT) against AI Factory AI for Dou Di Zhu. 84 5.14 Playing strength of ISMCTS against AI Factory AI for spades at the normal and maximum levels . 84 6.1 Information set search trees for the game shown in Figure 5.10 with partially observable moves. 93 6.2 Heat map showing the results of the LOTR:C playing strength experiment. 96 6.3 Results of the playing strength experiment for LOTR:C. 96 6.4 Heat map showing the results of the phantom 4; 4; 4-game playing strength experiment. 99 6.5 Results of the playing strength experiment for the phantom 4; 4; 4- game. 100 v 6.6 Average number of simulations performed in 1 second by deter- minized UCT, SO-ISMCTS and MO-ISMCTS. 103 6.7 Playing strength of determinized UCT and SO-ISMCTS for dif- ferent amounts of decision time playing Dou Di Zhu . 105 6.8 Playing strength of determinized UCT and MO-ISMCTS for.
Load more

Recommended publications
  • Ass Spielkarten
    Werbemittelkatalog www.werbespielkarten.com Spielkarten können das ASS im Ärmel sein ... Spielkarten als Werbemittel bleiben in Erinnerung – als kommunikatives Spielzeug werden sie entspannt in der Freizeit genutzt und eignen sich daher hervorragend als Werbe- und Informationsträger. Die Mischung macht‘s – ein beliebtes Spiel, qualitativ hochwertige Karten und Ihre Botschaft – eine vielversprechende Kombination! Inhalt Inhalt ........................................................................ 2 Unsere grüne Mission ............................... 2 Wo wird welches Blatt gespielt? ..... 3 Rückseiten ........................................................... 3 Brandneu bei ASS Altenburger ........ 4 Standardformate ........................................... 5 Kinderspiele ........................................................ 6 Verpackungen .................................................. 7 Quiz & Memo ................................................... 8 Puzzles & Würfelbecher ....................... 10 Komplettspiele .............................................. 11 Ideen ...................................................................... 12 Referenzen ....................................................... 14 Unsere grüne Mission Weil wir Kunden und Umwelt gleichermaßen verpflichtet sind ASS Altenburger will mehr erreichen, als nur seine geschäftlichen Ziele. Als Teil eines globalen Unternehmens sind wir davon überzeugt, eine gesellschaftliche Verantwortung für Erde, Umwelt und Menschen zu haben. Wir entscheiden uns bewusst
    [Show full text]
  • The Poetics of Reflection in Digital Games
    © Copyright 2019 Terrence E. Schenold The Poetics of Reflection in Digital Games Terrence E. Schenold A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2019 Reading Committee: Brian M. Reed, Chair Leroy F. Searle Phillip S. Thurtle Program Authorized to Offer Degree: English University of Washington Abstract The Poetics of Reflection in Digital Games Terrence E. Schenold Chair of the Supervisory Committee: Brian Reed, Professor English The Poetics of Reflection in Digital Games explores the complex relationship between digital games and the activity of reflection in the context of the contemporary media ecology. The general aim of the project is to create a critical perspective on digital games that recovers aesthetic concerns for game studies, thereby enabling new discussions of their significance as mediations of thought and perception. The arguments advanced about digital games draw on philosophical aesthetics, media theory, and game studies to develop a critical perspective on gameplay as an aesthetic experience, enabling analysis of how particular games strategically educe and organize reflective modes of thought and perception by design, and do so for the purposes of generating meaning and supporting expressive or artistic goals beyond amusement. The project also provides critical discussion of two important contexts relevant to understanding the significance of this poetic strategy in the field of digital games: the dynamics of the contemporary media ecology, and the technological and cultural forces informing game design thinking in the ludic century. The project begins with a critique of limiting conceptions of gameplay in game studies grounded in a close reading of Bethesda's Morrowind, arguing for a new a "phaneroscopical perspective" that accounts for the significance of a "noematic" layer in the gameplay experience that accounts for dynamics of player reflection on diegetic information and its integral relation to ergodic activity.
    [Show full text]
  • Enduring Gifts of Seasons Gone by WV Clubs Reach out to Share An
    PRSRT STD Love to * ECRWSS * US Postage Residential PAID Permit 162 Journey Unusual An Cus tomer Peoria, AZ Soulmates Found - Page 24 Page - Found Soulmates to Share Share to Out Reach Clubs WV Feast of Lights & Christmas Caring - Pages 20 and 33 33 and 20 Pages - Caring Christmas & Lights of Feast Seasons Gone By By Gone Seasons of Gifts Enduring More Blessed to Give - Pages 8 and 11 and 8 Pages - Give to Blessed More 39th Issue 39th December 2020 December $539,000 19456 N 87th Drive Vista Pinnacle MLS 6127556 Joy! WishingYou Home Staging IS KEY to a Great Sale! Lindsey Lori 602.828.1455 Shoultes Reiland December 2020 CONTENTSand FEATURES 7 Honoring John Schiff 8 Always Remembered 10 WV Veteran Treasure Page 16 11 WVA Reports A special Christmas memory 18 Cooking at WV 26 Posse News Deadline for submissions for the January issue is December 1st. Page 15 Kind strangers giving Call Judy Carrucciu at 623-321-2209 for advertising rates or send an email to: [email protected]. Disclaimer: Westbrook Village Living Magazine is independently owned and operated by Westbrook Living, Please also send all ideas, articles, club news L.L.C. It is not affiliated with the Westbrook Village Homeowners Association. No part of this publication may and memories to Judy. be reproduced without written consent of the publisher. Advertising does not constitute an endorsement of any product or service. Please independently investigate any Company that you do business with. Merchandise/ services are expected to be as advertised. Columns, articles, or advertising appearing in Westbrook Village This publication is delivered at the end of Living does not constitute endorsement by the Publisher of products, services or opinions advertised.
    [Show full text]
  • Learning Board Game Rules from an Instruction Manual Chad Mills A
    Learning Board Game Rules from an Instruction Manual Chad Mills A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science University of Washington 2013 Committee: Gina-Anne Levow Fei Xia Program Authorized to Offer Degree: Linguistics – Computational Linguistics ©Copyright 2013 Chad Mills University of Washington Abstract Learning Board Game Rules from an Instruction Manual Chad Mills Chair of the Supervisory Committee: Professor Gina-Anne Levow Department of Linguistics Board game rulebooks offer a convenient scenario for extracting a systematic logical structure from a passage of text since the mechanisms by which board game pieces interact must be fully specified in the rulebook and outside world knowledge is irrelevant to gameplay. A representation was proposed for representing a game’s rules with a tree structure of logically-connected rules, and this problem was shown to be one of a generalized class of problems in mapping text to a hierarchical, logical structure. Then a keyword-based entity- and relation-extraction system was proposed for mapping rulebook text into the corresponding logical representation, which achieved an f-measure of 11% with a high recall but very low precision, due in part to many statements in the rulebook offering strategic advice or elaboration and causing spurious rules to be proposed based on keyword matches. The keyword-based approach was compared to a machine learning approach, and the former dominated with nearly twenty times better precision at the same level of recall. This was due to the large number of rule classes to extract and the relatively small data set given this is a new problem area and all data had to be manually annotated.
    [Show full text]
  • Games and Rules
    Requirements for a General Game Mechanics Framework Imre Hofmann In this article I will apply a meta-theoretical approach to the question of how a game mechanics framework has to be designed in order to fulfil its task of ade- quately depicting or modeling the reality of game mechanics. I had two aims in mind when starting my research. I studied existing game theories and three game mechanics theories in particular in order to evaluate the state of the art of game mechanics theory. (Descriptive aim) The second aim followed on from these studies. With the results of my research I wanted to define the attributes a com- prehensive and general game mechanics theory might or – rather – needed to have. What are the general properties that such a theory should display? (Norma- tive aim) In my opinion the underlying mechanics of a game may be regarded in some way as its centerpiece. The reasons for this shall become clear over the course of this article. To begin with, I would like to make two terminological clarifications. First, I am not going to examine different game mechanics and typologies or categories of game mechanics. Instead, I will take a theoretical step backwards, so to speak, on the meta-level by analyzing and comparing different theories of game me- chanics (which themselves suggest categories and typologies). Secondly, I will use the expressions “game mechanics theory” “(game mechanics) framework” and “(game mechanics) model” synonymously. In my research I focused mainly on the following three key theories of game mechanics: 1. Carlo Fabricatore’s Gameplay and Game Mechanics Design (2007) 2.
    [Show full text]
  • Amazon Alive: a Decade of Discoveries 1999-2009
    Amazon Alive! A decade of discovery 1999-2009 The Amazon is the planet’s largest rainforest and river basin. It supports countless thousands of species, as well as 30 million people. © Brent Stirton / Getty Images / WWF-UK © Brent Stirton / Getty Images The Amazon is the largest rainforest on Earth. It’s famed for its unrivalled biological diversity, with wildlife that includes jaguars, river dolphins, manatees, giant otters, capybaras, harpy eagles, anacondas and piranhas. The many unique habitats in this globally significant region conceal a wealth of hidden species, which scientists continue to discover at an incredible rate. Between 1999 and 2009, at least 1,200 new species of plants and vertebrates have been discovered in the Amazon biome (see page 6 for a map showing the extent of the region that this spans). The new species include 637 plants, 257 fish, 216 amphibians, 55 reptiles, 16 birds and 39 mammals. In addition, thousands of new invertebrate species have been uncovered. Owing to the sheer number of the latter, these are not covered in detail by this report. This report has tried to be comprehensive in its listing of new plants and vertebrates described from the Amazon biome in the last decade. But for the largest groups of life on Earth, such as invertebrates, such lists do not exist – so the number of new species presented here is no doubt an underestimate. Cover image: Ranitomeya benedicta, new poison frog species © Evan Twomey amazon alive! i a decade of discovery 1999-2009 1 Ahmed Djoghlaf, Executive Secretary, Foreword Convention on Biological Diversity The vital importance of the Amazon rainforest is very basic work on the natural history of the well known.
    [Show full text]
  • American Skat : Or, the Game of Skat Defined : a Descriptive and Comprehensive Guide on the Rules and Plays of This Interesting
    'JTV American Skat, OR, THE GAME OF SKAT DEFINED. BY J. CHARLES EICHHORN A descriptive and comprehensive Guide on the Rules and Plays of if. is interesting game, including table, definition of phrases, finesses, and a full treatise on Skat as played to-day. CHICAGO BREWER. BARSE & CO. Copyrighted, January 21, 1898 EICHHORN By J. CHARLES SKAT, with its many interesting features and plays, has now gained such a firm foothold in America, that my present edition in the English language on this great game of cards, will not alone serve as a guide for beginners, but will be a complete compendium on this absorbing game. It is just a decade since my first book was pub- lished. During the past 10 years, the writer has visited, and been in personal touch with almost all the leading authorities on the game of Skat in Amer- ica as well as in Europe, besides having been contin- uously a director of the National Skat League, as well as a committeeman on rules. In pointing out the features of the game, in giving the rules, defining the plays, tables etc., I shall be as concise as possible, using no complicated or lengthy remarks, but in short and comprehensive manner, give all the points and information required. The game of Skat as played today according to the National Skat League values and rulings, with the addition of Grand Guckser and Passt Nicht as variations, is as well balanced a game, as the leading authorities who have given the same both thorough study and consideration, can make.
    [Show full text]
  • Download Booklet
    preMieRe Recording jonathan dove SiReNSONG CHAN 10472 siren ensemble henk guittart 81 CHAN 10472 Booklet.indd 80-81 7/4/08 09:12:19 CHAN 10472 Booklet.indd 2-3 7/4/08 09:11:49 Jonathan Dove (b. 199) Dylan Collard premiere recording SiReNSong An Opera in One Act Libretto by Nick Dear Based on the book by Gordon Honeycombe Commissioned by Almeida Opera with assistance from the London Arts Board First performed on 14 July 1994 at the Almeida Theatre Recorded live at the Grachtenfestival on 14 and 1 August 007 Davey Palmer .......................................... Brad Cooper tenor Jonathan Reed ....................................... Mattijs van de Woerd baritone Diana Reed ............................................. Amaryllis Dieltiens soprano Regulator ................................................. Mark Omvlee tenor Captain .................................................... Marijn Zwitserlood bass-baritone with Wireless Operator .................................... John Edward Serrano speaker Siren Ensemble Henk Guittart Jonathan Dove CHAN 10472 Booklet.indd 4-5 7/4/08 09:11:49 Siren Ensemble piccolo/flute Time Page Romana Goumare Scene 1 oboe 1 Davey: ‘Dear Diana, dear Diana, my name is Davey Palmer’ – 4:32 48 Christopher Bouwman Davey 2 Diana: ‘Davey… Davey…’ – :1 48 clarinet/bass clarinet Diana, Davey Michael Hesselink 3 Diana: ‘You mention you’re a sailor’ – 1:1 49 horn Diana, Davey Okke Westdorp Scene 2 violin 4 Diana: ‘i like chocolate, i like shopping’ – :52 49 Sanne Hunfeld Diana, Davey cello Scene 3 Pepijn Meeuws 5
    [Show full text]
  • Adversarial Search (Game)
    Adversarial Search CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2019 Soleymani “Artificial Intelligence: A Modern Approach”, 3rd Edition, Chapter 5 Most slides have been adopted from Klein and Abdeel, CS188, UC Berkeley. Outline } Game as a search problem } Minimax algorithm } �-� Pruning: ignoring a portion of the search tree } Time limit problem } Cut off & Evaluation function 2 Games as search problems } Games } Adversarial search problems (goals are in conflict) } Competitive multi-agent environments } Games in AI are a specialized kind of games (in the game theory) 3 Adversarial Games 4 Types of Games } Many different kinds of games! } Axes: } Deterministic or stochastic? } One, two, or more players? } Zero sum? } Perfect information (can you see the state)? } Want algorithms for calculating a strategy (policy) which recommends a move from each state 5 Zero-Sum Games } Zero-Sum Games } General Games } Agents have opposite utilities } Agents have independent utilities (values on outcomes) (values on outcomes) } Lets us think of a single value that one } Cooperation, indifference, competition, maximizes and the other minimizes and more are all possible } Adversarial, pure competition } More later on non-zero-sum games 6 Primary assumptions } We start with these games: } Two -player } Tu r n taking } agents act alternately } Zero-sum } agents’ goals are in conflict: sum of utility values at the end of the game is zero or constant } Perfect information } fully observable Examples: Tic-tac-toe,
    [Show full text]
  • The Penguin Book of Card Games
    PENGUIN BOOKS The Penguin Book of Card Games A former language-teacher and technical journalist, David Parlett began freelancing in 1975 as a games inventor and author of books on games, a field in which he has built up an impressive international reputation. He is an accredited consultant on gaming terminology to the Oxford English Dictionary and regularly advises on the staging of card games in films and television productions. His many books include The Oxford History of Board Games, The Oxford History of Card Games, The Penguin Book of Word Games, The Penguin Book of Card Games and the The Penguin Book of Patience. His board game Hare and Tortoise has been in print since 1974, was the first ever winner of the prestigious German Game of the Year Award in 1979, and has recently appeared in a new edition. His website at http://www.davpar.com is a rich source of information about games and other interests. David Parlett is a native of south London, where he still resides with his wife Barbara. The Penguin Book of Card Games David Parlett PENGUIN BOOKS PENGUIN BOOKS Published by the Penguin Group Penguin Books Ltd, 80 Strand, London WC2R 0RL, England Penguin Group (USA) Inc., 375 Hudson Street, New York, New York 10014, USA Penguin Group (Canada), 90 Eglinton Avenue East, Suite 700, Toronto, Ontario, Canada M4P 2Y3 (a division of Pearson Penguin Canada Inc.) Penguin Ireland, 25 St Stephen’s Green, Dublin 2, Ireland (a division of Penguin Books Ltd) Penguin Group (Australia) Ltd, 250 Camberwell Road, Camberwell, Victoria 3124, Australia
    [Show full text]
  • Best-First Minimax Search Richard E
    Artificial Intelligence ELSEVIER Artificial Intelligence 84 ( 1996) 299-337 Best-first minimax search Richard E. Korf *, David Maxwell Chickering Computer Science Department, University of California, Los Angeles, CA 90024, USA Received September 1994; revised May 1995 Abstract We describe a very simple selective search algorithm for two-player games, called best-first minimax. It always expands next the node at the end of the expected line of play, which determines the minimax value of the root. It uses the same information as alpha-beta minimax, and takes roughly the same time per node generation. We present an implementation of the algorithm that reduces its space complexity from exponential to linear in the search depth, but at significant time cost. Our actual implementation saves the subtree generated for one move that is still relevant after the player and opponent move, pruning subtrees below moves not chosen by either player. We also show how to efficiently generate a class of incremental random game trees. On uniform random game trees, best-first minimax outperforms alpha-beta, when both algorithms are given the same amount of computation. On random trees with random branching factors, best-first outperforms alpha-beta for shallow depths, but eventually loses at greater depths. We obtain similar results in the game of Othello. Finally, we present a hybrid best-first extension algorithm that combines alpha-beta with best-first minimax, and performs significantly better than alpha-beta in both domains, even at greater depths. In Othello, it beats alpha-beta in two out of three games. 1. Introduction and overview The best chess machines, such as Deep-Blue [lo], are competitive with the best humans, but generate billions of positions per move.
    [Show full text]
  • Hannah Arendt's Question and Human Rights Debates in Mao's
    Human Rights and Their Discontents: Hannah Arendt’s Question and Human Rights Debates in Mao’s China Wenjun Yu Human Rights and Their Discontents: Hannah Arendt’s Question and Human Rights Debates in Mao’s China Het onbehagen over mensenrechten: het probleem van Hannah Arendt en het debat over mensenrechten in het China van Mao (met een samenvatting in het Nederlands) Proefschrift ter verkrijging van de graad van doctor aan de Universiteit Utrecht op gezag van de rector magnificus, prof.dr. G.J. van der Zwaan, ingevolge het besluit van het college voor promoties in het openbaar te verdedigen op dinsdag 4 juli 2017 des middags te 12.45 uur door Wenjun Yu geboren op 3 april 1986 te Hubei, China Promotor: Prof.dr. I. de Haan Acknowledgements Writing a PhD dissertation is not a lonely work, I cannot finish this job without the generous help and supports from my supervisor, fellow PhD students, colleagues, friends and family. Although I take the complete responsibility for the content of this dissertation, I would like to thank all accompanies for their inspiration, encouragement, and generosity in the course of my PhD research. First and foremost, I would like to express my sincere gratitude to my supervisor Prof. Ido de Haan for his continuous support of my PhD work at Utrecht University, for his great concern over my life in the Netherlands, for his generous encouragements and motivations when I was frustrated by many research problems, and particularly when I was stuck in the way of writing the dissertation during my pregnancy and afterwards.
    [Show full text]