DOCSLIB.ORG

What Does AI's Success Playing Complex Board Games Tell

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
What Does AI's Success Playing Complex Board Games Tell OPINION What does AI’s success playing complex board games tell brain scientists? OPINION Dale Purvesa,1 In research, it sometimes happens that advances in one beat the European and world champions at Go (2, 3), a field unexpectedly inform another in a fundamental territorial board game far more complicated than chess. way. A case in point may be what computer-generated The latest version in this effort, called AlphaZero (4), now gameplay suggests about how brains operate. Spear- beats the best players—human or machine—in chess headed by Demis Hassabis, David Silver, and their and shogi (Japanese chess) as well as Go. colleagues at the artificial intelligence (AI) company That machines can beat expert human players in Google DeepMind, a series of articles published over board games is not news. The achievement of this the past several years has reported ongoing improve- long-standing goal in computer science first attracted ment of a computational strategy (1–3) that now beats widespread attention in 1997 when IBM’s program all players in complex board games (4). Beginning in “Deep Blue” beat Garry Kasparov, then the world 2015 with a computer program that beat human oppo- champion chess player (5). Human players have since nents at all 49 games in the Atari 2600 suite (challenges been shown to be weak opponents in such games that include Pong, Space Invaders, and Pac-Man) (1), compared with a variety of machine programs. What the group progressed to a program called AlphaGo that is different about Google DeepMind’s AlphaZero is Fig. 1. The search space of the territorial board game Go is intractable using logical algorithms. Image credit: Shutterstock/Saran Poroong. aDuke Institute for Brain Sciences, Duke University, Durham, NC 27708 The author declares no conflict of interest. Published under the PNAS license. Any opinions, findings, conclusions, or recommendations expressed in this work are those of the author and have not been endorsed by the National Academy of Sciences. 1Email: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1909565116 PNAS | July 23, 2019 | vol. 116 | no. 30 | 14785–14787 Downloaded by guest on September 30, 2021 that the system operates by learning on a wholly empirical is beyond reckoning, it clearly dwarfs the complexity (trial and error) basis. of board games such as Go. Previous game-playing machines, including earlier versions in the AlphaGo series, used a combination of “Intelligent” Brains? brute force logic, tree search, successful moves made In thinking how these facts bear on understanding by experts in response to specific board positions, and brains, some caution is in order when using phrases other “hand-crafted” expedients. In contrast, AlphaZero such as “artificial intelligence (AI).” Although we use the uses only the empirical results of self-play. The starting word “intelligence”—artificial or otherwise—as if we point is simply a randomly initialized “deep” neural net- knew what it meant, the term simply refers to the ability work (an artificial neural network with multiple hidden to solve some kind of problem. The presumption is that layers) that gradually improves by playing against itself AI solves problems the way humans do, ignoring the millions of times using only the rules of the game and fact that the way we solve problems is largely a mystery. reinforcement learning. With respect to humans, “intelligence” usually re- What, then, is the key to this success, and what are fers to skills most of us lack, such as the ability to do the implications for understanding of how human higher mathematics. But this usage is misleading: is brains work? The lesson seems to be that neural the accomplished athlete solving complex problems on success hinges on connectivity generated by trial- the playing field any less “intelligent” than the math and-error learning over evolutionary and individual prodigy? This definitional deficiency has led to endless time rather than algorithms that compute behavioral arguments, not least the value of IQ tests and other answers. dubious measures of a vague concept whose determi- nation is subject to social bias and other influences. The Underlying Strategy We researchers accord a high status to the ability To understand the power of this approach in playing to think through logical problems and imagine that is board games, consider the search spaces involved. what brains must be doing. Psychologists showed The “game tree complexity” of tic-tac-toe—i.e., an long ago, however, that systematic thinking is awkward estimate of the number of possible positions that must for humans with consequences that can be embarrassing be evaluated to determine the worth of an initial position— (7). For instance, when high school students were briefly is about 2 × 104. This number of possibilities is easily presented with the sequences searched by an algorithm, as my children learned at a 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 theme park when they were beaten by a chicken pecking one of the tic-tac-toe squares in what amounted to a and cleverly designed Skinner box. 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and asked to estimate the products, the median an- The take-home message may be that understanding swers given for the first series was 512 and for the neural circuitry in terms of steps specified by algorithms second 2,250. This result shows that when it comes to logic we are often flummoxed, in this case by failing to is not a path to success much beyond the challenge recognize that the sequences are multiplications of of tic-tac-toe. the same numbers and must, therefore, generate the same product (which is actually 40,320). Because ratio- nality and logic play little part in survival and reproduction, There are several different ways to measure the a generally feeble approach to problems such as this is complexity of more difficult board games, leading to what one might expect. These strategies are far too different estimates. But no matter the method used, as ponderous for generating answers to most biological the complexity of board games grows, the relevant problems, and problems whose solution demands rea- search spaces become unimaginably large. The game soning and logic are relatively rare outside the classroom. tree complexity is estimated to be about 1020 for checkers, about 10120 for chess, and an astonishing Implications 10320 for Go (6). For comparison, the estimated number AI in the guise of mimicking computations that brains of atoms in the universe is on the order of 1087.Unlike might be carrying out dates from a conference of math- tic-tac-toe, fully searching spaces of this magnitude is ematicians, computer scientists, information theo- not feasible. In the strategy used by Google DeepMind, rists, and others in 1956. The consensus was famously success follows not from a logical exploration of possible that this challenge should be relatively easy to solve. moves but from the instantiation of trial and error play More than 60 years on, however, the goal has not been in the network’s connectivity that beats a competing met. The central problem now as then is that no one machine playing in the same empirical way. knows what the operating principle of a brain actually is. The relevance of AlphaZero to neuroscience is the This may be where success in gameplay points the size of the search spaces organisms—and ultimately way. A wholly empirical approach to winning complex animals with brains—must contend with as they play board games revives a trial-and-error (neural network) “the game of life” by making “moves” that are rewarded approach that was introduced in the 1940s (8) but has by survival and reproductive success. Although the had a checkered history over the subsequent de- complexity of this biological “game tree” for humans cades (9). Solving problems by unsupervised learning 14786 | www.pnas.org/cgi/doi/10.1073/pnas.1909565116 Purves Downloaded by guest on September 30, 2021 using neural networks has often been overshadowed input board positions, the “synaptic weights” in the by the immense success of algorithmic computation network are updated based on the history of what (executing a series of specified steps), a strategy that worked well in millions of previous games. The Google has repeatedly proven its worth in applications as di- DeepMind group noted early on that the organization verse as manufacturing, genomics, and drug discovery. of networks thus trained bore little or no resemblance to But the success of reinforcement learning in tack- the organization of human brains (10). Indeed, the in- ling otherwise intractable games suggests that making scrutable connectivity of the trained AlphaZero net- behavioral responses based on what worked for a works may indicate why the detailed connectivity of species and its members over accumulated past ex- brains has failed to shed as much light on neural oper- perience is the most efficient way to win in life. Because ation as expected. the brain of any animal is the executor of behavioral The take-home message may be that understand- choices, it is hard to escape the implication that con- ing neural circuitry in terms of steps specified by al- tending with extremely large “search spaces” must be gorithms is not a path to success much beyond the predicated on neural (or machine) connectivity that re- flects accumulated learning by trial and error. This is, challenge of tic-tac-toe. If one accepts that playing after all, the strategy used in evolution. complex games empirically is a paradigm for playing If this empirical mode of operation is what brains the vastly more complex game of life, brain science such as ours are doing, then this game-related evidence could advance rapidly albeit in a framework different will have to be taken into account by brain scientists, from the rule-based computation that has often driven despite the daunting challenge of understanding nervous the field.
Load more

Recommended publications
  • Lecture Note on Deep Learning and Quantum Many-Body Computation
    Lecture Note on Deep Learning and Quantum Many-Body Computation Jin-Guo Liu, Shuo-Hui Li, and Lei Wang∗ Institute of Physics, Chinese Academy of Sciences Beijing 100190, China November 23, 2018 Abstract This note introduces deep learning from a computa- tional quantum physicist’s perspective. The focus is on deep learning’s impacts to quantum many-body compu- tation, and vice versa. The latest version of the note is at http://wangleiphy.github.io/. Please send comments, suggestions and corrections to the email address in below. ∗ [email protected] CONTENTS 1 introduction2 2 discriminative learning4 2.1 Data Representation 4 2.2 Model: Artificial Neural Networks 6 2.3 Cost Function 9 2.4 Optimization 11 2.4.1 Back Propagation 11 2.4.2 Gradient Descend 13 2.5 Understanding, Visualization and Applications Beyond Classification 15 3 generative modeling 17 3.1 Unsupervised Probabilistic Modeling 17 3.2 Generative Model Zoo 18 3.2.1 Boltzmann Machines 19 3.2.2 Autoregressive Models 22 3.2.3 Normalizing Flow 23 3.2.4 Variational Autoencoders 25 3.2.5 Tensor Networks 28 3.2.6 Generative Adversarial Networks 29 3.3 Summary 32 4 applications to quantum many-body physics and more 33 4.1 Material and Chemistry Discoveries 33 4.2 Density Functional Theory 34 4.3 “Phase” Recognition 34 4.4 Variational Ansatz 34 4.5 Renormalization Group 35 4.6 Monte Carlo Update Proposals 36 4.7 Tensor Networks 37 4.8 Quantum Machine Leanring 38 4.9 Miscellaneous 38 5 hands on session 39 5.1 Computation Graph and Back Propagation 39 5.2 Deep Learning Libraries 41 5.3 Generative Modeling using Normalizing Flows 42 5.4 Restricted Boltzmann Machine for Image Restoration 43 5.5 Neural Network as a Quantum Wave Function Ansatz 43 6 challenges ahead 45 7 resources 46 BIBLIOGRAPHY 47 1 1 INTRODUCTION Deep Learning (DL) ⊂ Machine Learning (ML) ⊂ Artificial Intelli- gence (AI).
    [Show full text]
  • AI Computer Wraps up 4-1 Victory Against Human Champion Nature Reports from Alphago's Victory in Seoul
    The Go Files: AI computer wraps up 4-1 victory against human champion Nature reports from AlphaGo's victory in Seoul. Tanguy Chouard 15 March 2016 SEOUL, SOUTH KOREA Google DeepMind Lee Sedol, who has lost 4-1 to AlphaGo. Tanguy Chouard, an editor with Nature, saw Google-DeepMind’s AI system AlphaGo defeat a human professional for the first time last year at the ancient board game Go. This week, he is watching top professional Lee Sedol take on AlphaGo, in Seoul, for a $1 million prize. It’s all over at the Four Seasons Hotel in Seoul, where this morning AlphaGo wrapped up a 4-1 victory over Lee Sedol — incidentally, earning itself and its creators an honorary '9-dan professional' degree from the Korean Baduk Association. After winning the first three games, Google-DeepMind's computer looked impregnable. But the last two games may have revealed some weaknesses in its makeup. Game four totally changed the Go world’s view on AlphaGo’s dominance because it made it clear that the computer can 'bug' — or at least play very poor moves when on the losing side. It was obvious that Lee felt under much less pressure than in game three. And he adopted a different style, one based on taking large amounts of territory early on rather than immediately going for ‘street fighting’ such as making threats to capture stones. This style – called ‘amashi’ – seems to have paid off, because on move 78, Lee produced a play that somehow slipped under AlphaGo’s radar. David Silver, a scientist at DeepMind who's been leading the development of AlphaGo, said the program estimated its probability as 1 in 10,000.
    [Show full text]
  • Accelerators and Obstacles to Emerging ML-Enabled Research Fields
    Life at the edge: accelerators and obstacles to emerging ML-enabled research fields Soukayna Mouatadid Steve Easterbrook Department of Computer Science Department of Computer Science University of Toronto University of Toronto [email protected] [email protected] Abstract Machine learning is transforming several scientific disciplines, and has resulted in the emergence of new interdisciplinary data-driven research fields. Surveys of such emerging fields often highlight how machine learning can accelerate scientific discovery. However, a less discussed question is how connections between the parent fields develop and how the emerging interdisciplinary research evolves. This study attempts to answer this question by exploring the interactions between ma- chine learning research and traditional scientific disciplines. We examine different examples of such emerging fields, to identify the obstacles and accelerators that influence interdisciplinary collaborations between the parent fields. 1 Introduction In recent decades, several scientific research fields have experienced a deluge of data, which is impacting the way science is conducted. Fields such as neuroscience, psychology or social sciences are being reshaped by the advances in machine learning (ML) and the data processing technologies it provides. In some cases, new research fields have emerged at the intersection of machine learning and more traditional research disciplines. This is the case for example, for bioinformatics, born from collaborations between biologists and computer scientists in the mid-80s [1], which is now considered a well-established field with an active community, specialized conferences, university departments and research groups. How do these transformations take place? Do they follow similar paths? If yes, how can the advances in such interdisciplinary fields be accelerated? Researchers in the philosophy of science have long been interested in these questions.
    [Show full text]
  • The Deep Learning Revolution and Its Implications for Computer Architecture and Chip Design
    The Deep Learning Revolution and Its Implications for Computer Architecture and Chip Design Jeffrey Dean Google Research [email protected] Abstract The past decade has seen a remarkable series of advances in machine learning, and in particular deep learning approaches based on artificial neural networks, to improve our abilities to build more accurate systems across a broad range of areas, including computer vision, speech recognition, language translation, and natural language understanding tasks. This paper is a companion paper to a keynote talk at the 2020 International Solid-State Circuits Conference (ISSCC) discussing some of the advances in machine learning, and their implications on the kinds of computational devices we need to build, especially in the post-Moore’s Law-era. It also discusses some of the ways that machine learning may also be able to help with some aspects of the circuit design process. Finally, it provides a sketch of at least one interesting direction towards much larger-scale multi-task models that are sparsely activated and employ much more dynamic, example- and task-based routing than the machine learning models of today. Introduction The past decade has seen a remarkable series of advances in machine learning (ML), and in particular deep learning approaches based on artificial neural networks, to improve our abilities to build more accurate systems across a broad range of areas [LeCun et al. 2015]. Major areas of significant advances ​ ​ include computer vision [Krizhevsky et al. 2012, Szegedy et al. 2015, He et al. 2016, Real et al. 2017, Tan ​ ​ ​ ​ ​ ​ and Le 2019], speech recognition [Hinton et al.
    [Show full text]
  • The Power and Promise of Computers That Learn by Example
    Machine learning: the power and promise of computers that learn by example MACHINE LEARNING: THE POWER AND PROMISE OF COMPUTERS THAT LEARN BY EXAMPLE 1 Machine learning: the power and promise of computers that learn by example Issued: April 2017 DES4702 ISBN: 978-1-78252-259-1 The text of this work is licensed under the terms of the Creative Commons Attribution License which permits unrestricted use, provided the original author and source are credited. The license is available at: creativecommons.org/licenses/by/4.0 Images are not covered by this license. This report can be viewed online at royalsociety.org/machine-learning Cover image © shulz. 2 MACHINE LEARNING: THE POWER AND PROMISE OF COMPUTERS THAT LEARN BY EXAMPLE Contents Executive summary 5 Recommendations 8 Chapter one – Machine learning 15 1.1 Systems that learn from data 16 1.2 The Royal Society’s machine learning project 18 1.3 What is machine learning? 19 1.4 Machine learning in daily life 21 1.5 Machine learning, statistics, data science, robotics, and AI 24 1.6 Origins and evolution of machine learning 25 1.7 Canonical problems in machine learning 29 Chapter two – Emerging applications of machine learning 33 2.1 Potential near-term applications in the public and private sectors 34 2.2 Machine learning in research 41 2.3 Increasing the UK’s absorptive capacity for machine learning 45 Chapter three – Extracting value from data 47 3.1 Machine learning helps extract value from ‘big data’ 48 3.2 Creating a data environment to support machine learning 49 3.3 Extending the lifecycle
    [Show full text]
  • ARCHITECTS of INTELLIGENCE for Xiaoxiao, Elaine, Colin, and Tristan ARCHITECTS of INTELLIGENCE
    MARTIN FORD ARCHITECTS OF INTELLIGENCE For Xiaoxiao, Elaine, Colin, and Tristan ARCHITECTS OF INTELLIGENCE THE TRUTH ABOUT AI FROM THE PEOPLE BUILDING IT MARTIN FORD ARCHITECTS OF INTELLIGENCE Copyright © 2018 Packt Publishing All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without the prior written permission of the publisher, except in the case of brief quotations embedded in critical articles or reviews. Every effort has been made in the preparation of this book to ensure the accuracy of the information presented. However, the information contained in this book is sold without warranty, either express or implied. Neither the author, nor Packt Publishing or its dealers and distributors, will be held liable for any damages caused or alleged to have been caused directly or indirectly by this book. Packt Publishing has endeavored to provide trademark information about all of the companies and products mentioned in this book by the appropriate use of capitals. However, Packt Publishing cannot guarantee the accuracy of this information. Acquisition Editors: Ben Renow-Clarke Project Editor: Radhika Atitkar Content Development Editor: Alex Sorrentino Proofreader: Safis Editing Presentation Designer: Sandip Tadge Cover Designer: Clare Bowyer Production Editor: Amit Ramadas Marketing Manager: Rajveer Samra Editorial Director: Dominic Shakeshaft First published: November 2018 Production reference: 2201118 Published by Packt Publishing Ltd. Livery Place 35 Livery Street Birmingham B3 2PB, UK ISBN 978-1-78913-151-2 www.packt.com Contents Introduction ........................................................................ 1 A Brief Introduction to the Vocabulary of Artificial Intelligence .......10 How AI Systems Learn ........................................................11 Yoshua Bengio .....................................................................17 Stuart J.
    [Show full text]
  • Technology Innovation and the Future of Air Force Intelligence Analysis
    C O R P O R A T I O N LANCE MENTHE, DAHLIA ANNE GOLDFELD, ABBIE TINGSTAD, SHERRILL LINGEL, EDWARD GEIST, DONALD BRUNK, AMANDA WICKER, SARAH SOLIMAN, BALYS GINTAUTAS, ANNE STICKELLS, AMADO CORDOVA Technology Innovation and the Future of Air Force Intelligence Analysis Volume 2, Technical Analysis and Supporting Material RR-A341-2_cover.indd All Pages 2/8/21 12:20 PM For more information on this publication, visit www.rand.org/t/RRA341-2 Library of Congress Cataloging-in-Publication Data is available for this publication. ISBN: 978-1-9774-0633-0 Published by the RAND Corporation, Santa Monica, Calif. © Copyright 2021 RAND Corporation R® is a registered trademark. Cover: U.S. Marine Corps photo by Cpl. William Chockey; faraktinov, Adobe Stock. Limited Print and Electronic Distribution Rights This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited. Permission is given to duplicate this document for personal use only, as long as it is unaltered and complete. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial use. For information on reprint and linking permissions, please visit www.rand.org/pubs/permissions. The RAND Corporation is a research organization that develops solutions to public policy challenges to help make communities throughout the world safer and more secure, healthier and more prosperous. RAND is nonprofit, nonpartisan, and committed to the public interest. RAND’s publications do not necessarily reflect the opinions of its research clients and sponsors.
    [Show full text]
  • Alpha-Beta Pruning
    Alpha-Beta Pruning Carl Felstiner May 9, 2019 Abstract This paper serves as an introduction to the ways computers are built to play games. We implement the basic minimax algorithm and expand on it by finding ways to reduce the portion of the game tree that must be generated to find the best move. We tested our algorithms on ordinary Tic-Tac-Toe, Hex, and 3-D Tic-Tac-Toe. With our algorithms, we were able to find the best opening move in Tic-Tac-Toe by only generating 0.34% of the nodes in the game tree. We also explored some mathematical features of Hex and provided proofs of them. 1 Introduction Building computers to play board games has been a focus for mathematicians ever since computers were invented. The first computer to beat a human opponent in chess was built in 1956, and towards the late 1960s, computers were already beating chess players of low-medium skill.[1] Now, it is generally recognized that computers can beat even the most accomplished grandmaster. Computers build a tree of different possibilities for the game and then work backwards to find the move that will give the computer the best outcome. Al- though computers can evaluate board positions very quickly, in a game like chess where there are over 10120 possible board configurations it is impossible for a computer to search through the entire tree. The challenge for the computer is then to find ways to avoid searching in certain parts of the tree. Humans also look ahead a certain number of moves when playing a game, but experienced players already know of certain theories and strategies that tell them which parts of the tree to look.
    [Show full text]
  • Machine Learning Conference Report
    Part of the conference series Breakthrough science and technologies Transforming our future Machine learning Conference report Machine learning report – Conference report 1 Introduction On 22 May 2015, the Royal Society hosted a unique, high level conference on the subject of machine learning. The conference brought together scientists, technologists and experts from across academia, industry and government to learn about the state-of-the-art in machine learning from world and UK experts. The presentations covered four main areas of machine learning: cutting-edge developments in software, the underpinning hardware, current applications and future social and economic impacts. This conference is the first in a new series organised This report is not a verbatim record, but summarises by the Royal Society, entitled Breakthrough Science the discussions that took place during the day and the and Technologies: Transforming our Future, which will key points raised. Comments and recommendations address the major scientific and technical challenges reflect the views and opinions of the speakers and of the next decade. Each conference will focus on one not necessarily that of the Royal Society. Full versions technology and cover key issues including the current of the presentations can be found on our website at: state of the UK industry sector, future direction of royalsociety.org/events/2015/05/breakthrough-science- research and the wider social and economic implications. technologies-machine-learning The conference series is being organised through the Royal Society’s Science and Industry programme, which demonstrates our commitment to reintegrate science and industry at the Society and to promote science and its value, build relationships and foster translation.
    [Show full text]
  • Arxiv:1709.02779V1 [Quant-Ph] 8 Sep 2017 I
    Machine learning & artificial intelligence in the quantum domain Vedran Dunjko Institute for Theoretical Physics, University of Innsbruck, Innsbruck 6020, Austria Max Planck Institute of Quantum Optics, Garching 85748, Germany Email: [email protected] Hans J. Briegel Institute for Theoretical Physics, University of Innsbruck Innsbruck 6020, Austria Department of Philosophy, University of Konstanz, Konstanz 78457, Germany Email: [email protected] Abstract. Quantum information technologies, on the one side, and intelligent learning systems, on the other, are both emergent technologies that will likely have a transforming impact on our society in the future. The respective underlying fields of basic research { quantum information (QI) versus machine learning and artificial intelligence (AI) { have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been prob- ing the question to what extent these fields can indeed learn and benefit from each other. QML explores the interaction between quantum computing and machine learning, inves- tigating how results and techniques from one field can be used to solve the problems of the other. In recent time, we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for machine learning problems, critical in our \big data" world. Conversely, machine learning already permeates many cutting-edge technologies, and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical machine learning optimization used in quantum experiments, quan- tum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents.
    [Show full text]
  • Combinatorial Game Theory
    Combinatorial Game Theory Aaron N. Siegel Graduate Studies MR1EXLIQEXMGW Volume 146 %QIVMGER1EXLIQEXMGEP7SGMIX] Combinatorial Game Theory https://doi.org/10.1090//gsm/146 Combinatorial Game Theory Aaron N. Siegel Graduate Studies in Mathematics Volume 146 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE David Cox (Chair) Daniel S. Freed Rafe Mazzeo Gigliola Staffilani 2010 Mathematics Subject Classification. Primary 91A46. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-146 Library of Congress Cataloging-in-Publication Data Siegel, Aaron N., 1977– Combinatorial game theory / Aaron N. Siegel. pages cm. — (Graduate studies in mathematics ; volume 146) Includes bibliographical references and index. ISBN 978-0-8218-5190-6 (alk. paper) 1. Game theory. 2. Combinatorial analysis. I. Title. QA269.S5735 2013 519.3—dc23 2012043675 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made by e-mail to [email protected]. c 2013 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government.
    [Show full text]
  • Game Tree Search
    CSC384: Introduction to Artificial Intelligence Game Tree Search • Chapter 5.1, 5.2, 5.3, 5.6 cover some of the material we cover here. Section 5.6 has an interesting overview of State-of-the-Art game playing programs. • Section 5.5 extends the ideas to games with uncertainty (We won’t cover that material but it makes for interesting reading). Fahiem Bacchus, CSC384 Introduction to Artificial Intelligence, University of Toronto 1 Generalizing Search Problem • So far: our search problems have assumed agent has complete control of environment • State does not change unless the agent (robot) changes it. • All we need to compute is a single path to a goal state. • Assumption not always reasonable • Stochastic environment (e.g., the weather, traffic accidents). • Other agents whose interests conflict with yours • Search can find a path to a goal state, but the actions might not lead you to the goal as the state can be changed by other agents (nature or other intelligent agents) Fahiem Bacchus, CSC384 Introduction to Artificial Intelligence, University of Toronto 2 Generalizing Search Problem •We need to generalize our view of search to handle state changes that are not in the control of the agent. •One generalization yields game tree search • Agent and some other agents. • The other agents are acting to maximize their profits • this might not have a positive effect on your profits. Fahiem Bacchus, CSC384 Introduction to Artificial Intelligence, University of Toronto 3 General Games •What makes something a game? • There are two (or more) agents making changes to the world (the state) • Each agent has their own interests • e.g., each agent has a different goal; or assigns different costs to different paths/states • Each agent tries to alter the world so as to best benefit itself.
    [Show full text]