General Game Playing

210 Pages·2014·2.045 MB·English

by  Michael Genesereth, Michael Thielscher

General Game Playing
Michael Genesereth
StanfordUniversity
Michael ielscher
UniversityofNewSouthWales
SYNTHESISLECTURESON
ARTIFICIALINTELLIGENCE
ANDMACHINE LEARNING#24
M
&C Morgan &cLaypool publishers
Copyright©2014byMorgan&Claypool
GeneralGamePlaying
MichaelGeneserethandMichaelielscher
www.morganclaypool.com
ISBN:9781627052559 paperback
ISBN:9781627052566 ebook
DOI10.2200/S00564ED1V01Y201311AIM024
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONARTIFICIALINTELLIGENCE
ANDMACHINELEARNING
Lecture#24
SeriesEditors:RonaldJ.Brachman,YahooResearch
WilliamW.Cohen,CarnegieMellonUniversity
PeterStone,UniversityofTexasatAustin
SeriesISSN
SynthesisLecturesonArtificialIntelligenceandMachineLearning
Print1939-4608 Electronic1939-4616
ABSTRACT
General game players are computer systems able to play strategy games based solely on formal
gamedescriptionssuppliedat“runtime”.(Inotherwords,theydon’tknowtherulesuntilthegame
starts.)Unlikespecializedgameplayers,suchasDeepBlue,generalgameplayerscannotrelyon
algorithmsdesignedinadvanceforspecificgames;theymustdiscoversuchalgorithmsthemselves.
General game playing expertise depends on intelligence on the part of the game player and not
justintelligenceoftheprogrammerofthegameplayer.
GGP is an interesting application in its own right. It is intellectually engaging and more
than a little fun. But it is much more than that. It provides a theoretical framework for model-
ing discrete dynamic systems and defining rationality in a way that takes into account problem
representation and complexities like incompleteness of information and resource bounds. It has
practicalapplicationsinareaswherethesefeaturesareimportant,e.g.,inbusinessandlaw.More
fundamentally, it raises questions about the nature of intelligence and serves as a laboratory in
whichtoevaluatecompetingapproachestoartificialintelligence.
isbookisanelementaryintroductiontoGeneralGamePlaying(GGP).(1)Itpresents
thetheoryofGeneralGamePlayingandleadingGGPtechnologies.(2)Itshowshowtocreate
GGPprogramscapableofcompetingagainstotherprogramsandhumans.(3)Itoffersaglimpse
ofsomeofthereal-worldapplicationsofGeneralGamePlaying.
KEYWORDS
generalgameplaying,artificialintelligence,logicprogramming,computationallogic,
intelligentagents,knowledgerepresentation
Contents
Preface ........................................................... xv
1 Introduction ....................................................... 1
1.1 Introduction ......................................................1
1.2 Games...........................................................2
1.3 GameDescription .................................................3
1.4 GameManagement ................................................7
1.5 GamePlaying.....................................................8
1.6 Discussion........................................................9
2 GameDescription.................................................. 13
2.1 Introduction .....................................................13
2.2 LogicPrograms ..................................................13
2.3 GameModel ....................................................17
2.4 GameDescriptionLanguage ........................................20
2.5 GameDescriptionExample.........................................21
2.6 GameSimulationExample .........................................24
2.7 GameRequirements...............................................27
2.8 PrefixGDL......................................................27
3 GameManagement ................................................ 31
3.1 Introduction .....................................................31
3.2 GameManagement ...............................................31
3.3 GameCommunicationLanguage ....................................32
3.4 GamePlay ......................................................33
4 GamePlaying ..................................................... 37
4.1 Introduction .....................................................37
4.2 Infrastructure ....................................................37
4.3 CreatingaLegalPlayer ............................................38
4.4 CreatingaRandomPlayer..........................................41
5 SmallSingle-PlayerGames .......................................... 43
5.1 Introduction .....................................................43
5.2 8-Puzzle ........................................................43
5.3 CompulsiveDeliberation ...........................................45
5.4 SequentialPlanning ...............................................46
6 SmallMultiple-PlayerGames ........................................ 51
6.1 Introduction .....................................................51
6.2 Minimax ........................................................51
6.3 BoundedMinimaxSearch ..........................................56
6.4 Alpha-BetaSearch ................................................59
7 HeuristicSearch ................................................... 67
7.1 Introduction .....................................................67
7.2 Depth-LimitedSearch.............................................67
7.3 Fixed-DepthHeuristicSearch .......................................68
7.4 VariableDepthHeuristicSearch .....................................70
8 ProbabilisticSearch ................................................ 75
8.1 Introduction .....................................................75
8.2 MonteCarloSearch...............................................75
8.3 MonteCarloTreeSearch...........................................78
9 PropositionalNets ................................................. 81
9.1 Introduction .....................................................81
9.2 PropositionalNets ................................................82
9.3 GamesasPropositionalNets ........................................85
10 GeneralGamePlayingWithPropnets ................................. 89
10.1 Introduction .....................................................89
10.2 PropositionalNetsasDataStructures .................................89
10.3 MarkingandReadingPropositionalNets ..............................92
10.4 ComputingGamePlayingBasics ....................................94
11 Factoring ......................................................... 97
11.1 Introduction .....................................................97
11.2 CompoundGameswithIndependentSubgames ........................98
11.3 CompoundGameswithInterdependentTermination ...................101
11.4 CompoundGameswithInterdependentActions .......................102
11.5 ConditionalIndependence.........................................104
12 DiscoveryofHeuristics ............................................ 107
12.1 Introduction ....................................................107
12.2 Latches ........................................................107
12.3 Inhibitors ......................................................108
12.4 DeadStateRemoval..............................................108
13 Logic ........................................................... 111
13.1 Introduction ....................................................111
13.2 Unification .....................................................111
13.3 DerivationSteps(withoutNegation).................................114
13.4 Derivations .....................................................115
13.5 DerivationTreeSearch............................................117
13.6 HandlingNegation ..............................................119
14 AnalyzingGameswithLogic ........................................ 129
14.1 Introduction ....................................................129
14.2 ComputingDomains .............................................129
14.3 ReducingtheDomainsFurther .....................................133
14.4 InstantiatingRules ...............................................137
14.5 AnalyzingtheStructureofGDLRules...............................139
14.6 RuleGraphs ....................................................139
14.7 UsingRuleGraphs...............................................142
14.7.1DeterminingtheEquivalenceofGameDescriptions ..............142
14.7.2ComputingSymmetries .....................................142
14.8 Exercises .......................................................145
15 SolvingSingle-PlayerGameswithLogic .............................. 151
15.1 AnswerSetProgramming .........................................151
15.2 AddingTimetoGDLRules .......................................152
15.3 SolvingSingle-PlayerGameswithAnswerSetProgramming .............156
15.4 SystemsforAnswerSetProgramming ...............................158
15.5 Exercises .......................................................158
16 DiscoveringHeuristicswithLogic ................................... 161
16.1 DiscoveringHeuristicswithAnswerSetProgramming ..................161
16.2 GoalHeuristics..................................................162
16.3 FuzzyLogic ....................................................163
16.4 UsingtheGoalHeuristics .........................................166
16.5 OptimizationsandLimitations .....................................167
16.6 Exercises .......................................................168
17 GameswithIncompleteInformation ................................. 171
17.1 Introduction ....................................................171
17.2 GDL-II .......................................................171
17.3 BlindTic-Tac-Toe ...............................................172
17.4 CardGamesandOthers ..........................................177
17.5 GDL-IIGameManagement.......................................178
17.6 PlayingGDL-IIGames:HypotheticalStates..........................180
17.7 SamplingCompleteStates.........................................181
17.8 Exercises .......................................................186
18 GameswithHistoricalConstraints ................................... 189
18.1 Introduction ....................................................189
18.2 SystemDefinitionLanguage .......................................189
18.3 Example–Tic-Tac-Toe ............................................190
18.4 Example–Chess .................................................194
19 IncompleteGameDescriptions...................................... 199
19.1 Introduction ....................................................199
19.2 RelationalLogic .................................................199
19.3 IncompleteGameDescriptionLanguage .............................203
19.4 ButtonsandLightsRevisited.......................................203
19.5 CompleteDescriptionofButtonsandLights ..........................205
19.6 IncompleteDescriptionofButtonsandLights.........................208
19.7 PlayingButtonsandLightswithanIncompleteDescription..............208
20 AdvancedGeneralGamePlaying .................................... 211
20.1 Introduction ....................................................211
20.2 TemporalGeneralGamePlaying ...................................211
20.3 InductiveGeneralGamePlaying....................................211
20.4 ReallyGeneralGamePlaying ......................................212
20.5 EnhancedGeneralGamePlaying ...................................212
Preface
General game players are computer systems able to play strategy games based solely on formal
gamedescriptionssuppliedat“runtime”.(Inotherwords,theydon’tknowtherulesuntilthegame
starts.)Unlikespecializedgameplayers,suchasDeepBlue,generalgameplayerscannotrelyon
algorithmsdesignedinadvanceforspecificgames;theymustdiscoversuchalgorithmsthemselves.
General game playing expertise depends on intelligence on the part of the game player and not
justintelligenceoftheprogrammerofthegameplayer.
GeneralGamePlaying(GGP)isaninterestingapplicationinitsownright.Itisintellec-
tuallyengagingandmorethanalittlefun.Butitismuchmorethanthat.Itprovidesatheoretical
frameworkformodelingdiscretedynamicsystemsandfordefiningrationalityinawaythattakes
intoaccountproblemrepresentationandcomplexitieslikeincompletenessofinformationandre-
source bounds. It has practical applications in areas where these features are important, e.g., in
business and law. More fundamentally, it raises questions about the nature of intelligence and
servesasalaboratoryinwhichtoevaluatecompetingapproachestoartificialintelligence.
isbookisanelementaryintroductiontoGeneralGamePlaying.(1)Itpresentsthetheory
of GGP and leading GGP technologies. (2) It shows how to create GGP programs capable of
competingagainstotherprogramsandhumans.(3)Itoffersaglimpseofsomeoftherealworld
applicationsofGeneralGamePlaying.
Althoughthebookiselementary,itdoesassumesomebasicbackground.Firstofall,readers
shouldbefamiliarwithSymbolicLogic.GamedescriptionsarewritteninthelanguageofSym-
bolic Logic, and it helps to be able to read and write such descriptions. Second, readers should
be familiar with the concepts of computer programming. At the very least, they should be able
toreadandunderstandprogramfragmentswritteninmodernprogramminglanguages.Weuse
Javascriptinallofourexamples.Javascriptisfairlysimple.Ifreadersarefamiliarwithlanguages
likeJavaandC,theyshouldbeabletoreadJavascriptwithoutanyfurthertraining.
Beforegettingstarted,wewanttoacknowledgethecontributionsofvariouspeople.Firstof
all,therearethevariousstudentswhoovertheyearshelpedtocraftthecourse,notablyNathaniel
Love, David Haley, Eric Schkufza, Evan Cox, Alex Landau, Peter Pham, Mirela Spasova, and
BertrandDecoster.SpecialmentiongoestoSamSchreiberformaintainingtheGGPconfigurable
player and the Java code base used by many students. He is also the creator and maintainer or
ggp.org,awebsiteforallthingsGGP.
And thanks as well to the students who over the years have had to endure early versions
ofthismaterial,inmanycaseshelpingtogetitrightbysufferingthroughexperimentsthatwere
not always successful. It is a testament to the intelligence of these students that they seem to
have learned the material despite multiple bumbling mistakes on our part. eir patience and
constructive comments were invaluable in helping us to understand what works and what does
not.
MichaelGeneserethandMichaelielscher
March2014