多智能体合作强化学习中的通信

warwick.ac.uk/lib-publications

AThesisSubmittedfortheDegreeofPhDattheUniversityofWarwick

PermanentWRAPURL:

http://wrap.warwick.ac.uk/179925

Copyrightandreuse:

Thisthesisismadeavailableonlineandisprotectedbyoriginalcopyright.Pleasescrolldowntoviewthedocumentitself.

Pleaserefertotherepositoryrecordforthisitemforinformationtohelpyoutociteit.Ourpolicyinformationisavailablefromtherepositoryhomepage.

Formoreinformation,pleasecontacttheWRAPTeamat:

wrap@warwick.ac.uk

WARW

THEUNIVERSITYOFWARWICK

LearningtoCommunicateinCooperativeMulti-Agent

ReinforcementLearning

by

EmanuelePesce

Thesis

SubmittedtotheUniversityofWarwick

inpartialfulfilmentoftherequirements

foradmissiontothedegreeof

DoctorofPhilosophyinEngineering

WarwickManufacturingGroup

February2023

i

Contents

ListofTables

iv

ListofFigures

v

Acknowledgments

viii

Declarations

ix

1Publications

ix

2Sponsorshipsandgrants

x

Abstract

xi

Acronyms

xii

Chapter1Introduction

1

1.1Researchobjectives

3

1.2Contributions

3

1.3Outline

4

Chapter2LiteratureReview

5

2.1Reinforcementlearning

6

2.2Deepreinforcementlearning

8

2.3Multi-agentdeepreinforcementlearning

9

2.4Cooperativemethods

12

2.5Emergenceofcommunication

13

2.6Communicationmethods

14

ii

2.6.1Attentionmechanismstosupportcommunication

17

2.6.2Graph-basedcommunicationmechanisms

18

Chapter3Memory-drivencommunication

20

3.1Introduction

20

3.2Memory-drivenMADDPG

22

3.2.1Problemsetup

22

3.2.2Memory-drivencommunication

23

3.2.3MD-MADDPGdecentralisedexecution

29

3.3Experimentalsettings

29

3.3.1Environments

29

3.4Experimentalresults

32

3.4.1Mainresults

32

3.4.2Implementationdetails

35

3.4.3Increasingthenumberofagents

36

3.5Communicationanalysis

37

3.6Ablationstudies

41

3.6.1Investigatethememorycomponents

41

3.6.2Corruptingthememory

42

3.6.3Multipleseeds

44

3.6.4Multiplememorysizes

47

3.7Summary

47

Chapter4Connectivity-drivencommunication

49

4.1Introduction

49

4.2Connectivity-drivencommunication

52

4.2.1Problemsetup

52

4.2.2Learningthedynamiccommunicationgraph

52

4.2.3Learningatime-dependentattentionmechanism

54

4.2.4Heatkernel:additionaldetailsandanillustration

56

4.2.5Reinforcementlearningalgorithm

58

4.3Experimentalsettings

61

4.3.1Environments

61

iii

4.3.2Implementationdetails

64

4.4Experimentalresults

65

4.4.1Mainresults

65

4.4.2Varyingthenumberofagents

71

4.5Communicationanalysis

72

4.6Ablationstudies

78

4.6.1Investigatingtheheat-kernelcomponents

78

4.6.2Heat-kernelthreshold

79

4.7Summary

80

Chapter5BenchmarkingMARLmethodsforcooperativemis-

sionsofunmannedaerialvehicles

82

5.1Introduction

82

5.2Proposeddroneenvironment

84

5.3Competingalgorithms

87

5.4Experimentalsettings

92

5.5Experimentalresults

94

5.6Discussion

96

5.7Summary

97

Chapter6Conclusionsandfuturework

98

6.1Conclusion

98

6.2Futurework

100

6.3Ethicalimplications

102

iv

ListofTables

3.1ComparingMD-MADDPGwithotherbaselines

33

3.2Increasingthenumberofagents-CooperativeNavigation

36

3.3Increasingthenumberofagents-POCooperativeNavigation

.37

3.4AblationstudyonMD-MADDPGcomponents

43

3.5Corruptingthememorycontent

43

4.1ComparingCDCwithotherbasilnes

66

4.2ComparivesummaryofMARLalgorithms

67

4.3Varyingthenumberofagents

71

4.4Graphanalysis

75

4.5Heat-kernelthreshold

80

5.1Commonparametersoftheenvironments

86

5.2SummaryofselectedMARLalgorithms

92

5.3Environmentparameters

93

5.4Benchmarkingresults

94

v

ListofFigures

2.1Reinforcementlearning

7

2.2MADDPG

11

3.1TheMD-MADDPGframework

24

3.2Environmentillustrations

32

3.3Learnedcommunicationstrategies-write

38

3.4Learnedcommunicationstrategy-read

41

3.5ChangingseedsonSwappingCooperativeNavigation

45

3.6ChangingseedsonSequentialCooperativeNavigation

46

3.7Investigatingdifferentmemorydimensions

47

4.1TheCDCframework

53

4.2Anedgeselectionexample

58

4.3Enviromentillustrations

63

4.4Learningcurves-NavigationControlandLineControl

69

4.5Learningcurves-FormationControlandDynamicPackControl

70

4.6Communicationnetworks-NavigationControlandLineControl

73

4.7Communicationnetworks-FormationControlandDynamic

PackControl

74

4.8Averagecommunicationgraphs-NavigationControlandLine

Control

76

4.9Averagecommunicationgraphs-FormationControlandDy-

namicPackControl

77

4.10AblationstudyonCDCcomponents

79

vi

5.1AUVrepresentation

86

5.2Learningcurves

96

TomybelovedSimona,fortheendlesslove,care,andsupportthroughoutalltheseyearstogether,andforbelievinginmemorethananyoneelse.

viii

Acknowledgments

Thisthesiswouldnothavebeenpossiblewithoutthehelpandsupportofmanypeople.Firstly,IwouldliketoexpressmygratitudetoProfessorGiovanniMontanaandtheWMGdepartmentforgrantingmetheopportunitytopursueafully-fundedPhDattheUniversityofWarwick.IamthankfultoGiovanniforhisguidancethroughoutthisjourney,consistentlyprovidingmewithusefuladviceandcontributingtotherevisionofmymanuscripts.Additionally,IamgratefultoKurtDebattistaforhissupportovertheyears.IwouldalsoliketoextendmythankstoLukeOwenandRamonDalmau-CodinafortheircontributionstothedevelopmentoftheUAVenvironment.IwouldliketoacknowledgeJeremieHoussineauandRaúlSantos-Rodríguez,myexaminers,fortheirvaluableadvicetoenhancethisthesis.AbigthankyougoestoProfessorTonyMcNallyforhisassistanceincoordinatingtheexaminationprocess.IalsowishtoextendmythankstoProfessorRobertoTagliaferriforbeingasourceofinspirationandinstillinginmealoveforthisfield.

Furthermore,IwishtothankallthefriendsIhavehadtheprivilegeofmeetingalongthispath.Ruggiero,withwhomIhavesharedcountlessmemorablemomentsandtechnicaldiscussions.Demetris,forhisencouragementandinspirationeverytimeIneededit.IamalsothankfultoKevin,Massimo,Ozsel,SaadandFrancesco,allofwhomhaveplayedsignificantrolesinmakingthisPhDjourneyamoreenjoyableandsociableexperience.

Finally,Iamincrediblygratefultomyparents,RoccoandRita,foralwaysbelievinginmeandencouragingmetobewhoIam.AspecialthanksgoestoSimona,mybelovedpartner,whoisthemostcaringpersonIhavemetandhasconsistentlybeenasourceofsupportduringbothjoyfulandchallengingtimes.

ix

Declarations

ThisthesisissubmittedtotheUniversityofWarwickinsupportofmyapplic-ationforthedegreeofDoctorofPhilosophy.Ithasbeencomposedbymyselfandhasnotbeensubmittedinanypreviousapplicationforanydegree.

1Publications

Partsofthisthesishavebeenpreviouslypublishedbytheauthorinthefollowing:

[125]

EmanuelePesceandGiovanniMontana.Improvingcoordinationinsmall-scalemulti-agentdeepreinforcementlearningthroughmemory-drivencommunication.MachineLearning,109(9):1727–1747,2020

[126]

EmanuelePesceandGiovanniMontana.Learningmulti-agentcoordin-ationthroughconnectivity-drivencommunication.MachineLearning,2022.doi:10.1007/s10994-022-06286-6

[127]

EmanuelePesce,RamonDalmau,LukeOwen,andGiovanniMontana.Benchmarkingmulti-agentdeepreinforcementlearningforcooperativemissionsofunmannedaerialvehicles.InProceedingsoftheInternationalWorkshoponCitizen-CentricMultiagentSystems,pages49–56.CMAS,2023

Alltheworkpublished

[125

–

127

]islicensedunderaCreativeCommonsAttribution4.0InternationalLicense.Toviewacopyofthislicencevisit

/licenses/by/4.0/.

x

2Sponsorshipsandgrants

ThisresearchwasfundedbytheUniversityofWarwick.

xi

Abstract

Recentadvancesindeepreinforcementlearninghaveproducedunpreceden-tedresults.Thesuccessobtainedonsingle-agentapplicationsledtoexploringthesetechniquesinthecontextofmulti-agentsystemswhereseveraladditionalchallengesneedtobeconsidered.Communicationhasalwaysbeencrucialtoachievingcooperationinmulti-agentdomainsandlearningtocommunicaterepresentsafundamentalmilestoneformulti-agentreinforcementlearningalgorithms.Inthisthesis,differentmulti-agentreinforcementlearningap-proachesareexplored.Theseprovidearchitecturesthatarelearnedend-to-endandcapableofachievingeffectivecommunicationprotocolsthatcanboostthesystemperformanceincooperativesettings.Firstly,weinvestigateanovelapproachwhereintra-agentcommunicationhappensthroughasharedmemorydevicethatcanbeusedbytheagentstoexchangemessagesthroughlearnablereadandwriteoperations.Secondly,weproposeagraph-basedapproachwhereconnectivitiesareshapedbyexchangingpairwisemessageswhicharethenaggregatedthroughanovelformofattentionmechanismbasedonagraphdiffusionmodel.Finally,wepresentanewsetofenvironmentswithreal-worldinspiredconstraintsthatweutilisetobenchmarkthemostrecentstate-of-the-artsolutions.Ourresultsshowthatcommunicationcanbeafundamentaltooltoovercomesomeoftheintrinsicdifficultiesthatcharacterisecooperativemulti-agentsystems.

xii

Acronyms

CDCConnectivity-drivencommunication.

CLDECentralisedlearningdecentralisedexecution.

CNCooperativenavigation.

DDPGDeepdeterministicpolicygradient.

DNNDeepneuralnetwork.

DPGDeterministicpolicygradient.

DQNDeepQ-network.

DRLDeepreinforcementlearning.

ERExperiencereplay.

GNNGraphneuralnetwork.

HKHeatkernel.

KLKullback-Leibler.

LSTMLongshorttermmemory.

MAMulti-agent.

MADRLMulti-agentdeepreinforcementlearning.

MA-MADDPGMeta-agentMADDPG.

MADDPGMulti-agentDDPG.

xiii

MARLMulti-agentreinforcementlearning.

MD-MADDPGMemory-drivenMADDPG.

MDPMarkovdecisionprocess.

NNNeuralnetwork.

PCPrincipalcomponent.

PCAPrincipalcomponentanalysis.

PGPolicygradient.

POPartialobservability.

PPOProximalpolicyoptimization.

RLReinforcementlearning.

RNNRecurrentneuralnetwork.

TRPOTrustregionpolicyoptimisation.

UASUnmannedaerialsystem.

VDNValuedecompositionnetwork.

1

Chapter1

Introduction

ReinforcementLearning(RL)allowsagentstolearnhowtomapobservationstoactionsthroughfeedbackrewardsignals[

157]

.Recently,deepneuralnetworks(DNNs)

[89,

141

]havehadanoticeableimpactonRL

[94]

.Theyprovideflexiblemodelsforlearningvaluefunctionsandpolicies,overcomedifficultiesrelatedtolargestatespaces,andeliminatetheneedforhand-craftedfeaturesandad-hocheuristics

[29,

121,

122]

.Deepreinforcementlearning(DRL)algorithms,whichusuallyrelyondeepneuralnetworkstoapproximatefunctions,havebeensuccessfullyemployedinsingle-agentsystems,includingvideogameplaying

[111

],robotlocomotion

[97

],objectlocalisation[

18

]anddata-centercooling

[38]

.FollowingtheuptakeofDRLinsingle-agentdomains,thereisnowaneedtodevelopimprovedlearningalgorithmsformulti-agent(MA)systemswhereadditionalchallengesarise.Multi-agentreinforcementlearning(MARL)extendsRLtoproblemscharacterizedbytheinterplayofmultipleagentsoperatinginasharedenvironment.Thisisascenariothatistypicalofmanyreal-worldapplicationsincludingrobotnavigation[

162

],autonomousvehiclescoordination

[15

],trafficmanagement

[36

],andsupplychainmanagement

[90]

.Comparedtosingle-agentsystems,MARLpresentsadditionallayersofcomplexity.Earlyapproachesstartedexploringhowdeepreinforcementlearningtechniquescanbeutilisedinmulti-agentsettings[

23,

53,

155

],whereitemergedaneedofnoveltechniquesspecificallydesignedtotackleMAchallenges.

2

MarkovDecisionProcesses(MDP),uponwhichDRLmethodsrely,assumethattherewarddistributionanddynamicsarestationary[

58]

.Whenmultiplelearnersinteractwitheachother,thispropertyisviolatedbecausetherewardthatanagentreceivesalsodependsonotheragents’actions[

86]

.Thisissue,knownasthemoving-targetproblem

[166

],removesconvergenceguaranteesandintroducesadditionallearninginstabilities.Furtherdifficultiesarisefromenvironmentscharacterizedbypartialobservability[

23,

128,

151

]wherebytheagentsdonothavefullaccesstotheworldstate,andwherecoordinationskillsareessential.

Animportantchallengeinmulti-agentdeepreinforcementlearning(MADRL)ishowtofacilitatecommunicationamonginteractingagents.Communicationiswidelyknowntoplayacriticalroleinpromotingcoordinationbetweenhumans

[159]

.Humanshavebeenproventoexcelatcommunicatingeveninabsenceofaconventionalcode[

32]

.Whencoordinationisrequiredandnocommonlanguagesexist,simplecommunicationprotocolsarelikelytoemerge

[144]

.Humancommunicationinvolvesmorethansendingandreceivingmes-sages,itrequiresspecializedinteractiveintelligencewherereceivershavetheabilitytorecognizeintentionsandsenderscanproperlydesignmessages[

178]

.Theemergenceofcommunicationhasbeenwidelyinvestigated[

47,

163

],forexamplenewsignsandsymbolscanemergewhenitcomestorepresentingrealconcepts.Fusarolietal.

[46]

demonstratedthatlanguagecanbeseenasasocialcoordinationdevicelearntthroughreciprocalinteractionwiththeenvironmentforoptimizingcoordinativedynamics.Therelationbetweencommunicationandcoordinationhasbeenwidelydiscussed[

34,

71,

109,

170]

.Communicationisanessentialskillinmanytasks:forinstance,incriticalsituations,whereisoffundamentalimportanceinproperlymanagingcriticalandurgentsitu-ations,suchasemergencyresponseorganizations[

28

],inwhichiscrucialtoestablishaclearwayofcommunicating.Forexample,inordertoproperlymanagecriticalandurgentsituations,emergencyresponseorganizationsneedaclearcommunicationthatisfundamentalandcanbeachievedthroughsharinginformationamongstdifferentagentsinvolved,whichisusuallyaccomplishedthroughyearsofcommontraining

[28]

.Inmultiplayervideogames,itisoften

3

essentialtoreachasufficientlyhighlevelofcoordinationrequiredtosucceed,oftenacquiredviacommunicating[

20]

.WebelievethatcommunicationisapromisingtoolthatneedstobeexploitedbyMADRLmodelsinordertoenhancetheirperformanceinmulti-agentenvironments.Whenthisresearchwasstarted,wenoticedalackofmethodstoenableinter-agentcommunication,sowedecidedtoexplorethisareatocontributetofillingagapthathadthepotentialforimprovingthecollaborationprocessinaMAsystem.

1.1Researchobjectives

TheaimofthisresearchistoexplorenovelcommunicationmodelstoenhancetheperformanceofexistingMARLmethods.Inparticular,wefocusoncooper-ativescenarios,whichiswherecommunicationisneededthemostbytheagentsinordertoproperlysucceedandcompletetheassignedtasks.Weinvestigatedifferentapproachestoachievingeffectivewaysofcommunicatingtoboostthelevelofcooperationinmulti-agentsettings.Theresultingcommunicationprotocolsarelearnedend-to-endsothat,attrainingtime,theycanbeadaptedbytheagentstoovercomethedifficultiesproposedbytheunderlyingenviron-mentalconfiguration.Inaddition,wealsoaimtoanalysethecontentofthelearnedcommunicationcontent.

1.2Contributions

Themaincontributionsmadeinthisthesisaresummarisedasfollows:

•inChapter

3

,weproposeanovelmulti-agentapproachwhereinter-agentcommunicationisobtainedbyprovidingacentralisedsharedmemorythateachagenthastolearntouseinordertoreadandwritemessagesfortheothersinsequentialorder;

•inChapter

4

,wediscussanovelmulti-agentmodelthatfirstconstructsagraphofconnectivitiestoencodepair-wisemessageswhicharethenusedtogenerateanagent-specificsetofencodingsthroughaproposed

4

attentionmechanismthatutilisesadiffusionmodelsuchastheheat-kernel(HK);

•inChapter

5

,weproposeanenvironmenttosimulatedronebehavioursinrealisticsettingsandpresentarangeofexperimentsinordertoevaluatetheperformanceofseveralstate-of-the-artmethodsinsuchscenarios.

1.3Outline

Thissectionprovidesanoutlineofthisthesis.Therestofthisdocumentisstructuredasfollows.Chapter

2

reviewstheexistingMADRLmodelsthatrelatetothiswork,withaspecialfocusoncooperativealgorithms.Chapter

3

introducesthefirstresearchcontributionthatproposesanovelformofcommunicationbasedonasharedmemorycell.Chapter

4

presentsthesecondresearchcontributioninwhichagraphbasedarchitectureisexploitedbyadiffusionmodeltogenerateagentspecificmessages.Chapter

5

proposesanovelenvironmenttosimulatearealisticscenarioofdronenavigationanddiscussesanextensivecomparisonofseveralstate-of-the-artMADRLmodels.Chapter

6

concludesthisworkwithadiscussionoftheresultsobtainedandrecommendationsforfuturework.

5

Chapter2

LiteratureReview

Inthischapter,weintroducetheRLsettingandreviewtheexistingworksrelatedtomulti-agentreinforcementlearning.InSection

2.2

,wediscusssignificantmilestonesinsingle-agentreinforcementlearningtoestablishthefoundationalknowledgefortheextendedorutilizedbasiclearningtechniques.Section

2.2

presentsdeeplearningextensionsforthepreviouslymentionedapproaches,servingasaconnectionbetweensingle-agentandmulti-agentmethodologies.MovingontoSection

2.3

,wefocusonhowtheseapproacheshavebeenexpandedtooperateinmulti-agentscenarios,withaparticularemphasisonthetrainingphasesthatarecommonlyemployedinstate-of-the-artworks.Wethencategorizethemulti-agentliteratureintothefollowinggroups:

•Cooperativemethods(Section

2.4

):worksthatconcentrateonachievingcooperationbetweenagents

•Emergenceofcommunication(Section

2.5

):worksthatinvestigatehowautonomousagentscanlearnlanguages

•Communicationmethods(Section

2.6

):workswhereagentsmustlearntocommunicatetoenhancesystemperformance

Inthisreview,weintentionallyomittedspecificresearchareassuchastraditionalgametheoryapproaches[

120,

123,

145

],microgridsystems[

27,

70,

72

],andprogrammingforparallelexecutionsofagents[

24,

45,

136]

.Our

6

primaryfocuswasonmulti-agentworksbasedonreinforcementlearningapproaches,withaparticularemphasisoncommunicationmethodologies.

Someofthemethodsmentionedinthisreviewhavealsobeenchosenasbaselinesfortheexperimentspresentedinthesubsequentchapters,particularlyinChapter

5

,thatplaysacrucialroleasitservesasapracticalcontextfortheproposedmulti-agentapproachesdiscussedinChapters

3

and

4.

Byintroducingaspecificallydesignedenvironmenttosimulatedronebehavioursinrealisticsettings,Chapter

5

providesindeedapracticalplatformforevaluatingtheperformanceofstate-of-the-artMADRLmodelsthatemploydifferentcommunicationandcoordinationmethodsdiscussedinthischapter.

2.1Reinforcementlearning

Reinforcementlearningmethodsformalisetheinteractionofanagent(oractor)withitsenvironmentsusingaMarkovdecisionprocess[

129]

.AnMDPisdefinedasatuple〈S,A,R,T,γ〉whereSisthesetthatcontainsallthestatesofagivenenvironment,Aisasetoffiniteactionsthatcanbeselectedbytheagent,andtherewardfunctionR:S×A→Rdefinesrewardreceivedbyanagentwhenexecutingtheactiona∈Awhilebeinginastates∈S.AtransitionfunctionT:S×Adescribeshowtheenvironmentdeterminesthenextstatewhenstartingfromastates∈Sandgivenanactiona∈A.Thediscountfactorγbalancesthetrade-offbetweencurrentandfuturerewards.AsrepresentedinFigure

2.1

,anagentinteractswiththeenvironmentbyproducinganactiongiventhecurrentstateandreceivingarewardinreturn.MDPsaresuitablemodelstotakedecisionsinfullyobservableenvironmentswhereacompletedescriptionofallitselementsisavailabletotheagentsandcanbeexploitedbytechniquessuchasthevalueiterationalgorithm[

9]

whichiterativelycomputesavaluefunctionthatestimatesthepotentialrewardfunctionofeachstate.Astate-actionvalueinsteadiscalculatedwhenthepotentialrewardfunctionisestimatedusingboththestateandtheaction.WhenaMDPissolvedastochasticpolicyπ:S×A→[0,1]isobtainedtomapstatesintoactions.RLalgorithmsoftenmakeuseofthepastagents’

7

Figure2.1:Areinforcementlearningsetting.Theenvironmentprovidesanobservationwhiletheagentproducesanactionandreceivesarewardinreturn.

experiencewithinteractingwiththeenvironment.Awell-knownalgorithmistheQ-learning

[176

],atabularapproachthatkeepstrackoftheQ-functionsQ(s,a)thatestimatethediscountedsumoffuturerewardforagivenpairstate-action.Everytimetheagentmovesfromastatesintoastates’usinganactiona’therespectivetabularentryisupdatedasfollows:

Q(s,a)=Q(s,a)+α[(r+γmaxQ(s’,a’))−Q(s,a)](2.1)

a,

whereα∈[0,1]isthelearningrate.

Policygradients(PG)methods[

157

]representanalternativeapproachofQ-learningwheretheparametersθofthepolicyaredirectlyadjustedtominimisetheobjectivefunctionbytakingstepsinthedirectionofthegradientfinedastheγ-discountedsumofrewardsandt∈{1,...T}isthetime-stepoftheenvironment.Suchgradientiscalculatedasfollows:

▽θJ(θ)=Ea~πθ[▽θlogπθ(a|s)Q(s,a)](2.2)

TheREINFORCEalgorithm

[179

]utilisesEq.

2.2

inconjunctionwithaMonteCarloestimationoffullsampledtrajectoriestolearnpolicyparametersinthe

8

followingway:

(2.3)

Policygradientalgorithmsarerenownedtosufferfromhighvariancewhichcansignificantlyslowthelearningprocess[

79]

.Thisissueisoftenmitigatedbyaddingabaseline,suchastheaveragerewardorthestatevaluefunction,thataimstocorrectthehighvariationattrainingtime.Actor-criticmethods[

79]

arecomposedofanactormodulethatselectstheactionstotakeandacriticthatprovidesthefeedbacknecessaryforthelearningprocess.Whenthecriticisabletolearnboththestate-actionandthevaluefunctions,anadvantagefunctioncanbecalculatedasthedifferencebetweenthesetwoestimates.Apopularactor-criticalgorithmistheDeterministicPolicyGradient(DPG)

[149

],inwhichtheactorisupdatedthroughthegradientofthepolicy,whilethecriticutilisesthestandardQ-learningapproach.InDPGthepolicyisassumedtobeadeterministicfunctionμθ:S→Aandthegradientthatminimisestheobjectivefunctioncanbewrittenas:

▽θJ(θ)=Es~D[▽θμθ(a|s)▽aQ(s,a)Ia=μθ(s)](2.4)

whereDisanexperiencereplay(ER)bufferthatstoresthehistoricaltransitions,μθandQ(s,a)representtheactorandthecritic,respectively.

2.2Deepreinforcementlearning

Deeplearningtechniques

[89

]havewidelybeenadoptedtoovercomethemajorlimitationsoftraditionalreinforcementlearningalgorithms,suchaslearninginenvironmentswithlargestatespacesorhavingtoprovidehand-specifiedfeatures

[158]

.Deepneuralnetworks(DNN)asfunctionapproximatorsallowedindeedtoapproximatevaluefunctionsandagents’policies[

12]

.InDQN

[110

],theQ-learningframeworkisextendedwithDNNs,inordertoapproximatethestateprovidedbytheenvironment,whilestillkeepingthehistoricalexperienceinanexperiencereplaybufferwhichisusedsampledataattrainingtime.DQNlearnstoapproximatet