By David Anderson SZTAKI (Budapest, Hungary) WPI D2009
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ByDavidAndersonSZTAKI(Budapest,Hungary)WPID2009
1997,DeepBluewonagainstKasparov AverageworkstationcandefeatbestChessplayers
ComputerChessnolonger“interesting” Goismuchharderforcomputerstoplay
Branchingfactoris~50‐200versus~35inChess Positionalevaluationinaccurate,expensive Gamecannotbescoreduntiltheend
BeginnerscandefeatbestGoprograms
Two‐player,totalinformation Playerstaketurnsplacingblackandwhitestonesongrid
Boardis19x19(13x13or9x9forbeginners) Objectistosurroundemptyspaceasterritory Piecescanbecaptured,butnotmoved Winnerdeterminedbymostpoints(territorypluscapturedpieces)
Imagefromhttp://ict.ewi.tudelft.nl/~gineke/
Minimax/α‐βalgorithmsrequirehugetrees Treedepthcannotbecuteasily
Monte‐Carlonowmorepopular Simulaterandomgamesfromthegametree Useresultstopickbestmove
Twoareasofoptimization Discoveryofgoodpathsinthegametree Intelligenceofrandomsimulations▪ Randomgamesareusuallybogus
Needtobalancebetweenexploration… Discoveringandsimulatingnewpaths
Andexploitation… Simulatingthemostoptimalpath
BestmethodiscurrentlyUCTgivenbyLeventeKocsisandCsabaSzepesvári.
Sayyouhaveaslotmachinewithaprobabilityofgivingyoumoney.Youcaninferthisprobabilitythroughexperimentation.
Whatiftherearethreeslotmachines,andeachhasadifferentprobability?
Youneedtochoosebetweenexperimenting(exploration)andgettingthebestreward(exploitation).
UCBalgorithmbalancestheseproblemstominimizelossofreward.
UCTappliesUCBtogameslikeGo,decidingwhichmovetoexplorenextbytreatingitlikethebanditproblem.
Startswithone‐leveltreeoflegalboardmoves
PicksbestmoveaccordingtoUCBalgorithm
RunsMonte‐Carlosimulation,updatenode’swin/loss.
ThisisoneiterationoftheUCTprocess.
Ifnodegetsvisitedenoughtimes,startlookingatitschildmoves
UCTdivesdeeper,eachtimepickingthemost“interesting”move.
Eventually,UCThasbuiltalargetreeofsimulationinformation
UCTisnowinmostmajorcompetitiveprograms
“MoGo”usedUCTtodefeataprofessional Used800‐nodegridanda9stonehandicap
Muchresearchnowfocusedonimprovingsimulationintelligence
Policydecideswhichmovetoplaynextinarandomgamesimulation
HighstochasticitymakesUCTlessaccurate Takeslongertoconvergetocorrectmove
ToomuchdeterminismmakesUCTlesseffective DefeatspurposeofMonte‐Carlosearch Mightintroduceharmfulselectionbias
CertainshapesinGoaregood “Hane”hereisastrongattackonB
Othersarequitebad! B’s“emptytriangle”istoodenseandwasteful
MoGousespatternknowledgewithUCT Hand‐crafteddatabaseof3x3interestingpatterns Doubledsimulationwin‐rateaccordingtoauthors
Canpatternknowledgebetrainedautomaticallyviamachinelearning?
Paper“Monte‐CarloSimulationBalancing” (byDavidSilverandGeraldTesauro) Policiesaccumulateerrorwitheachmove Strongpoliciesminimizethiserror,butnotthewhole‐gameerror
Proposesalgorithmsforminimizingwhole‐gameerrorwitheachmove
Authorstestedon5x5Gousing2x2patterns Foundthatbalancingwasmoreeffectiveoverrawstrength
Implementedpattern‐learningalgorithmsin“Monte‐CarloSimulationBalancing” Strength:Apprenticeship Strength:PolicyGradientReinforcement Balance:PolicyGradientSimulationBalancing Balance:Two‐StepSimulationBalancing
Used9x9Gowith3x3patterns
Usedamateurdatabaseof9x9gamesfortraining
Mention‐worthymetrics: Simulationwinrateagainstpurelyrandom UCTwinrateagainstUCTpurelyrandom UCTwinrateagainstGNUGo
Simplestalgorithm Looksateverymoveofeverygameinthetrainingset Highpreferenceforchosenmoves Lowpreferenceforunchosenmoves
Stronglyfavoredgoodpatterns Over‐training;poorerrorcompensation
Valuesconvergetoinfinity
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Playout UCTvslibEGO UCTvsGNUGo
Winrate(%
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GameType
ApprenticeshipvsPureRandom
PureRandom
Apprenticeship
Playsrandomgamesfromthetrainingset Ifthesimulationmatchestheoriginalgameresult,patternsgethigherpreference
Otherwise,lowerpreference Resultswerepromising
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ReinforcementvsPureRandom
PureRandom
Reinforcement
Foreachtraininggame… Playsrandomgamestoestimatewinrate Playsmorerandomgamestodeterminewhichpatternswinandlose
Givespreferencestopatternsbasedonerrorbetweenactualgameresultandobservedwinrate
Usually,stronglocalmoves Seemedtolearngoodpatterndistribution Aggressivelyplayeduselessmoveshopingforanopponentmistake
Poorconsiderationofthewholeboard
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GameType
SimulationBalancingversusPureRandom
PureRandom
SimulationBalancing
Picksrandomgamestates Computesscoreestimateofeverymoveat2‐plydepth
Updatespatternpreferencesbasedontheseresults,usingactualgameresulttocompensateforerror
Gamescoreishardtoestimate,usuallyinaccurate
Extremelyexpensive;10‐30sectoestimatescore
Gamescoredoesn’tchangemeaningfullyformanymoves
Probablydoesnotscaleasboardsizegrows
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Playout UCTvslibEGO UCTvsGNUGo
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TwoStepBalancingvsPureRandom
PureRandom
TwoStepBalancing
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AlgorithmResults
PureRandom
Apprenticeship
Reinforcement
SimulationBalancing
TwoStepBalancing
Reinforcementstrongest Allalgorithmscapableofverydeterministicpolicies
HigherplayoutwinratesweretoodeterministicandthususuallybadwithUCT
Gomaybetoocomplexforthesealgorithms Optimizingself‐playdoesn’tguaranteegoodmoves
LeventeKocsis
SZTAKI
ProfessorsSárközyandSelkow
Algorithmgenerateslistofpatterns Eachpatternhasaweight/value Policylooksatopenpositionsontheboard Getsthepatternateachopenposition Usesweightsasaprobabilitydistribution
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