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Multi-agent coordination : a reinforcement learning approach / Arup Kumar Sadhu, Amit Konar.

By: Sadhu, Arup Kumar [author.].
Contributor(s): Konar, Amit [author.] | IEEE Xplore (Online Service) [distributor.] | Wiley [publisher.].
Material type: materialTypeLabelBookPublisher: Hoboken, New Jersey : Wiley-IEEE, [2021]Distributor: [Piscataqay, New Jersey] : IEEE Xplore, [2020]Description: 1 PDF.Content type: text Media type: electronic Carrier type: online resourceISBN: 9781119698999.Subject(s): Reinforcement learning | Multiagent systemsGenre/Form: Electronic books.Additional physical formats: Print version:: Multi-agent coordinationDDC classification: 006.3/1 Online resources: Abstract with links to resource Also available in print.
Contents:
PREFACE -- ACKNOWLEDGEMENT -- CHAPTER 1 INTRODUCTION: MULTI-AGENT COORDINATION BY REINFORCEMENT LEARNING AND EVOLUTIONARY ALGORITHMS 1 -- 1.1 INTRODUCTION 2 -- 1.2 SINGLE AGENT PLANNING 3 -- 1.2.1 Terminologies used in single agent planning 4 -- 1.2.2 Single agent search-based planning algorithms 9 -- 1.2.2.1 Dijkstra's algorithm 10 -- 1.2.2.2 A* (A-star) Algorithm 12 -- 1.2.2.3 D* (D-star) Algorithm 14 -- 1.2.2.4 Planning by STRIPS-like language 16 -- 1.2.3 Single agent reinforcement learning 16 -- 1.2.3.1 Multi-Armed Bandit Problem 17 -- 1.2.3.2 Dynamic programming and Bellman equation 19 -- 1.2.3.3 Correlation between reinforcement learning and Dynamic programming 20 -- 1.2.3.4 Single agent Q-learning 20 -- 1.2.3.5 Single agent planning using Q-learning 23 -- 1.3 MULTI-AGENT PLANNING AND COORDINATION 24 -- 1.3.1 Terminologies related to multi-agent coordination 24 -- 1.3.2 Classification of multi-agent system 25 -- 1.3.3 Game theory for multi-agent coordination 27 -- 1.3.3.1 Nash equilibrium (NE) 30 -- 1.3.3.1.1 Pure strategy NE (PSNE) 31 -- 1.3.3.1.2 Mixed strategy NE (MSNE) 33 -- 1.3.3.2 Correlated equilibrium (CE) 36 -- 1.3.3.3 Static game examples 37 -- 1.3.4 Correlation among RL, DP, and GT 39 -- 1.3.5 Classification of MARL 39 -- 1.3.5.1 Cooperative multi-agent reinforcement learning 41 -- 1.3.5.1.1 Static 41 -- Independent Learner (IL) and Joint Action Learner (JAL) 41Frequency maximum Q-value (FMQ) heuristic 44 -- 1.3.5.1.2 Dynamic 46 -- Team-Q 46 -- Distributed -Q 47 -- Optimal Adaptive Learning 50 -- Sparse cooperative Q-learning (SCQL) 52 -- Sequential Q-learning (SQL) 53 -- Frequency of the maximum reward Q-learning (FMRQ) 53 -- 1.3.5.2 Competitive multi-agent reinforcement learning 55 -- 1.3.5.2.1 Minimax-Q Learning 55 -- 1.3.5.2.2 Heuristically-accelerated multi-agent reinforcement learning 56 -- 1.3.5.3 Mixed multi-agent reinforcement learning 57 -- 1.3.5.3.1 Static 57 -- Belief-based Learning rule 57 -- Fictitious play 57 -- Meta strategy 58 -- Adapt When Everybody is Stationary, Otherwise Move to Equilibrium (AWESOME) 60.
Hyper-Q 62 -- Direct policy search based 63 -- Fixed learning rate 63 -- Infinitesimal Gradient Ascent (IGA) 63 -- Generalized Infinitesimal Gradient Ascent (GIGA) 65 -- Variable learning rate 66 -- Win or Learn Fast-IGA (WoLF-IGA) 66 -- GIGA-Win or Learn Fast (GIGA-WoLF) 66 -- 1.3.5.3.2 Dynamic 67 -- Equilibrium dependent 67 -- Nash-Q Learning 67 -- Correlated-Q Learning (CQL) 68 -- Asymmetric-Q Learning (AQL) 68 -- Friend-or-Foe Q-learning 70 -- Negotiation-based Q-learning 71 -- MAQL with equilibrium transfer 74 -- Equilibrium independent 76 -- Variable learning rate 76 -- Win or Learn Fast Policy hill-climbing (WoLF-PHC) 76 -- Policy Dynamic based Win or Learn Fast (PD-WoLF) 78 -- Fixed learning rate 78 -- Non-Stationary Converging Policies (NSCP) 78 -- Extended Optimal Response Learning (EXORL) 79 -- 1.3.6 Coordination and planning by MAQL 80 -- 1.3.7 Performance analysis of MAQL and MAQL-based coordination 81 -- 1.4 COORDINATION BY OPTIMIZATION ALGORITHM 83 -- 1.4.1 Particle Swarm Optimization (PSO) Algorithm 84 -- 1.4.2 Firefly Algorithm (FA) 87 -- 1.4.2.1 Initialization 87 -- 1.4.2.2 Attraction to Brighter Fireflies 87 -- 1.4.2.3 Movement of Fireflies 88 -- 1.4.3 Imperialist Competitive Algorithm (ICA) 89 -- 1.4.3.1 Initialization 89 -- 1.4.3.2 Selection of Imperialists and Colonies 89 -- 1.4.3.3 Formation of Empires 89 -- 1.4.3.4 Assimilation of Colonies 90 -- 1.4.3.5 Revolution 91 -- 1.4.3.6 Imperialistic Competition 91 -- 1.4.3.6.1 Total Empire Power Evaluation 91 -- 1.4.3.6.2 Reassignment of Colonies and Removal of Empire 92 -- 1.4.3.6.3 Union of Empires 92 -- 1.4.4 Differential evolutionary (DE) algorithm 93 -- 1.4.4.1 Initialization 93 -- 1.4.4.2 Mutation 93 -- 1.4.4.3 Recombination 93 -- 1.4.4.4 Selection 93 -- 1.4.5 Offline optimization 94 -- 1.4.6 Performance analysis of optimization algorithms 94 -- 1.4.6.1 Friedman test 94 -- 1.4.6.2 Iman-Davenport test 95 -- 1.5 SCOPE OF THE Book 95 -- 1.6 SUMMARY 98 -- References 98 -- CHAPTER 2 IMPROVE CONVERGENCE SPEED OF MULTI-AGENT Q-LEARNING FOR COOPERATIVE TASK-PLANNING 107.
2.1 INTRODUCTION 108 -- 2.2 LITERATURE REVIEW 112 -- 2.3 PRELIMINARIES 114 -- 2.3.1 Single agent Q-learning 114 -- 2.3.2 Multi-agent Q-learning 115 -- 2.4 PROPOSED MULTI-AGENT Q-LEARNING 118 -- 2.4.1 Two useful properties 119 -- 2.5 PROPOSED FCMQL ALGORITHMS AND THEIR CONVERGENCE ANALYSIS 120 -- 2.5.1 Proposed FCMQL algorithms 120 -- 2.5.2 Convergence analysis of the proposed FCMQL algorithms 121 -- 2.6 FCMQL-BASED COOPERATIVE MULTI-AGENT PLANNING 122 -- 2.7 EXPERIMENTS AND RESULTS 123 -- 2.8 CONCLUSIONS 130 -- 2.9 SUMMARY 131 -- 2.10 APPENDIX 2.1 131 -- 2.11 APPENDIX 2.2 135 -- References 152 -- CHAPTER 3 CONSENSUS Q-LEARNING FOR MULTI-AGENT COOPERATIVE PLANNING 157 -- 3.1 INTRODUCTION 158 -- 3.2 PRELIMINARIES 159 -- 3.2.1 Single agent Q-learning 159 -- 3.2.2 Equilibrium-based multi-agent Q-learning 160 -- 3.3 CONSENSUS 161 -- 3.4 PROPOSED CONSENSUS Q-LEARNING AND PLANNING 162 -- 3.4.1 Consensus Q-learning 162 -- 3.4.2 Consensus-based multi-robot planning 164 -- 3.5 EXPERIMENTS AND RESULTS 165 -- 3.5.1 Experimental setup 165 -- 3.5.2 Experiments for CoQL 165 -- 3.5.3 Experiments for consensus-based planning 166 -- 3.6 CONCLUSIONS 168 -- 3.7 SUMMARY 168 -- References 168 -- CHAPTER 4 AN EFFICIENT COMPUTING OF CORRELATED EQUILIBRIUM FOR COOPERATIVE Q-LEARNING BASED MULTI-AGENT PLANNING 171 -- 4.1 INTRODUCTION 172 -- 4.2 SINGLE-AGENT Q-LEARNING AND EQUILIBRIUM BASED MAQL 175 -- 4.2.1 Single Agent Q learning 175 -- 4.2.2 Equilibrium based MAQL 175 -- 4.3 PROPOSED COOPERATIVE MULTI-AGENT Q-LEARNING AND PLANNING 176 -- 4.3.1 Proposed schemes with their applicability 176 -- 4.3.2 Immediate rewards in Scheme-I and -II 177 -- 4.3.3 Scheme-I induced MAQL 178 -- 4.3.4 Scheme-II induced MAQL 180 -- 4.3.5 Algorithms for scheme-I and II 182 -- 4.3.6 Constraint QL-I/ QL-II(C ......................................................... 183 -- 4.3.7 Convergence 183 -- Multi-agent planning 185 -- 4.4 COMPLEXITY ANALYSIS 186 -- 4.4.1 Complexity of Correlated Q-Learning 187 -- 4.4.1.1 Space Complexity 187.
4.4.1.2 Time Complexity 187 -- 4.4.2 Complexity of the proposed algorithms 188 -- 4.4.2.1 Space Complexity 188 -- 4.4.2.2 Time Complexity 188 -- 4.4.3 Complexity comparison 189 -- 4.4.3.1 Space complexity 190 -- 4.4.3.2 Time complexity 190 -- 4.5 SIMULATION AND EXPERIMENTAL RESULTS 191 -- 4.5.1 Experimental platform 191 -- 4.5.1.1 Simulation 191 -- 4.5.1.2 Hardware 192 -- 4.5.2 Experimental approach 192 -- 4.5.2.1 Learning phase 193 -- 4.5.2.2 Planning phase 193 -- 4.5.3 Experimental results 194 -- 4.6 CONCLUSION 201 -- 4.7 SUMMARY 202 -- 4.8 APPENDIX 203 -- References 209 -- CHAPTER 5 A MODIFIED IMPERIALIST COMPETITIVE ALGORITHM FOR MULTI-AGENT STICK- CARRYING APPLICATION 213 -- 5.1 INTRODUCTION 214 -- 5.2 PROBLEM FORMULATION FOR MULTI-ROBOT STICK-CARRYING 219 -- 5.3 PROPOSED HYBRID ALGORITHM 222 -- 5.3.1 An Overview of Imperialist Competitive Algorithm (ICA) 222 -- 5.3.1.1 Initialization 222 -- 5.3.1.2 Selection of Imperialists and Colonies 223 -- 5.3.1.3 Formation of Empires 223 -- 5.3.1.4 Assimilation of Colonies 223 -- 5.3.1.5 Revolution 224 -- 5.3.1.6 Imperialistic Competition 224 -- 5.3.1.6.1 Total Empire Power Evaluation 225 -- 5.3.1.6.2 Reassignment of Colonies and Removal of Empire 225 -- 5.3.1.6.3 Union of Empires 226 -- 5.4 AN OVERVIEW OF FIREFLY ALGORITHM (FA) 226 -- 5.4.1 Initialization 226 -- 5.4.2 Attraction to Brighter Fireflies 226 -- 5.4.3 Movement of Fireflies 227 -- 5.5 PROPOSED IMPERIALIST COMPETITIVE FIREFLY ALGORITHM 227 -- 5.5.1 Assimilation of Colonies 229 -- 5.5.1.1 Attraction to Powerful Colonies 230 -- 5.5.1.2 Modification of Empire Behavior 230 -- 5.5.1.3 Union of Empires 230 -- 5.6 SIMULATION RESULTS 232 -- 5.6.1 Comparative Framework 232 -- 5.6.2 Parameter Settings 232 -- 5.6.3 Analysis on Explorative Power of ICFA 232 -- 5.6.4 Comparison of Quality of the Final Solution 233 -- 5.6.5 Performance Analysis 233 -- 5.7 COMPUTER SIMULATION AND EXPERIMENT 240 -- 5.7.1 Average total path deviation (ATPD) 240 -- 5.7.2 Average Uncovered Target Distance (AUTD) 241.
5.7.3 Experimental Setup in Simulation Environment 241 -- 5.7.4 Experimental Results in Simulation Environment 242 -- 5.7.5 Experimental Setup with Khepera Robots 244 -- 5.7.6 Experimental Results with Khepera Robots 244 -- 5.8 CONCLUSION 245 -- 5.9 SUMMARY 247 -- 5.10 APPENDIX 5.1 248 -- References 249 -- CHAPTER 6 CONCLUSIONS AND FUTURE DIRECTIONS 255 -- 6.1 CONCLUSIONS 256 -- 6.2 FUTURE DIRECTIONS 257.
Summary: "This book explores the usage of Reinforcement Learning for Multi-Agent Coordination. Chapter 1 introduces fundamentals of the multi-robot coordination. Chapter 2 offers two useful properties, which have been developed to speed-up the convergence of traditional multi-agent Q-learning (MAQL) algorithms in view of the team-goal exploration, where team-goal exploration refers to simultaneous exploration of individual goals. Chapter 3 proposes the novel consensus Q-learning (CoQL), which addresses the equilibrium selection problem. Chapter 4 introduces a new dimension in the literature of the traditional correlated Q-learning (CQL), in which correlated equilibrium (CE) is computed partly in the learning and the rest in the planning phases, thereby requiring CE computation once only. Chapter 5 proposes an alternative solution to the multi-agent planning problem using meta-heuristic optimization algorithms. Chapter 6 provides the concluding remarks based on the principles and experimental results acquired in the previous chapters. Possible future directions of research are also examined briefly at the end of the chapter."-- Provided by publisher.
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Includes bibliographical references and index.

PREFACE -- ACKNOWLEDGEMENT -- CHAPTER 1 INTRODUCTION: MULTI-AGENT COORDINATION BY REINFORCEMENT LEARNING AND EVOLUTIONARY ALGORITHMS 1 -- 1.1 INTRODUCTION 2 -- 1.2 SINGLE AGENT PLANNING 3 -- 1.2.1 Terminologies used in single agent planning 4 -- 1.2.2 Single agent search-based planning algorithms 9 -- 1.2.2.1 Dijkstra's algorithm 10 -- 1.2.2.2 A* (A-star) Algorithm 12 -- 1.2.2.3 D* (D-star) Algorithm 14 -- 1.2.2.4 Planning by STRIPS-like language 16 -- 1.2.3 Single agent reinforcement learning 16 -- 1.2.3.1 Multi-Armed Bandit Problem 17 -- 1.2.3.2 Dynamic programming and Bellman equation 19 -- 1.2.3.3 Correlation between reinforcement learning and Dynamic programming 20 -- 1.2.3.4 Single agent Q-learning 20 -- 1.2.3.5 Single agent planning using Q-learning 23 -- 1.3 MULTI-AGENT PLANNING AND COORDINATION 24 -- 1.3.1 Terminologies related to multi-agent coordination 24 -- 1.3.2 Classification of multi-agent system 25 -- 1.3.3 Game theory for multi-agent coordination 27 -- 1.3.3.1 Nash equilibrium (NE) 30 -- 1.3.3.1.1 Pure strategy NE (PSNE) 31 -- 1.3.3.1.2 Mixed strategy NE (MSNE) 33 -- 1.3.3.2 Correlated equilibrium (CE) 36 -- 1.3.3.3 Static game examples 37 -- 1.3.4 Correlation among RL, DP, and GT 39 -- 1.3.5 Classification of MARL 39 -- 1.3.5.1 Cooperative multi-agent reinforcement learning 41 -- 1.3.5.1.1 Static 41 -- Independent Learner (IL) and Joint Action Learner (JAL) 41Frequency maximum Q-value (FMQ) heuristic 44 -- 1.3.5.1.2 Dynamic 46 -- Team-Q 46 -- Distributed -Q 47 -- Optimal Adaptive Learning 50 -- Sparse cooperative Q-learning (SCQL) 52 -- Sequential Q-learning (SQL) 53 -- Frequency of the maximum reward Q-learning (FMRQ) 53 -- 1.3.5.2 Competitive multi-agent reinforcement learning 55 -- 1.3.5.2.1 Minimax-Q Learning 55 -- 1.3.5.2.2 Heuristically-accelerated multi-agent reinforcement learning 56 -- 1.3.5.3 Mixed multi-agent reinforcement learning 57 -- 1.3.5.3.1 Static 57 -- Belief-based Learning rule 57 -- Fictitious play 57 -- Meta strategy 58 -- Adapt When Everybody is Stationary, Otherwise Move to Equilibrium (AWESOME) 60.

Hyper-Q 62 -- Direct policy search based 63 -- Fixed learning rate 63 -- Infinitesimal Gradient Ascent (IGA) 63 -- Generalized Infinitesimal Gradient Ascent (GIGA) 65 -- Variable learning rate 66 -- Win or Learn Fast-IGA (WoLF-IGA) 66 -- GIGA-Win or Learn Fast (GIGA-WoLF) 66 -- 1.3.5.3.2 Dynamic 67 -- Equilibrium dependent 67 -- Nash-Q Learning 67 -- Correlated-Q Learning (CQL) 68 -- Asymmetric-Q Learning (AQL) 68 -- Friend-or-Foe Q-learning 70 -- Negotiation-based Q-learning 71 -- MAQL with equilibrium transfer 74 -- Equilibrium independent 76 -- Variable learning rate 76 -- Win or Learn Fast Policy hill-climbing (WoLF-PHC) 76 -- Policy Dynamic based Win or Learn Fast (PD-WoLF) 78 -- Fixed learning rate 78 -- Non-Stationary Converging Policies (NSCP) 78 -- Extended Optimal Response Learning (EXORL) 79 -- 1.3.6 Coordination and planning by MAQL 80 -- 1.3.7 Performance analysis of MAQL and MAQL-based coordination 81 -- 1.4 COORDINATION BY OPTIMIZATION ALGORITHM 83 -- 1.4.1 Particle Swarm Optimization (PSO) Algorithm 84 -- 1.4.2 Firefly Algorithm (FA) 87 -- 1.4.2.1 Initialization 87 -- 1.4.2.2 Attraction to Brighter Fireflies 87 -- 1.4.2.3 Movement of Fireflies 88 -- 1.4.3 Imperialist Competitive Algorithm (ICA) 89 -- 1.4.3.1 Initialization 89 -- 1.4.3.2 Selection of Imperialists and Colonies 89 -- 1.4.3.3 Formation of Empires 89 -- 1.4.3.4 Assimilation of Colonies 90 -- 1.4.3.5 Revolution 91 -- 1.4.3.6 Imperialistic Competition 91 -- 1.4.3.6.1 Total Empire Power Evaluation 91 -- 1.4.3.6.2 Reassignment of Colonies and Removal of Empire 92 -- 1.4.3.6.3 Union of Empires 92 -- 1.4.4 Differential evolutionary (DE) algorithm 93 -- 1.4.4.1 Initialization 93 -- 1.4.4.2 Mutation 93 -- 1.4.4.3 Recombination 93 -- 1.4.4.4 Selection 93 -- 1.4.5 Offline optimization 94 -- 1.4.6 Performance analysis of optimization algorithms 94 -- 1.4.6.1 Friedman test 94 -- 1.4.6.2 Iman-Davenport test 95 -- 1.5 SCOPE OF THE Book 95 -- 1.6 SUMMARY 98 -- References 98 -- CHAPTER 2 IMPROVE CONVERGENCE SPEED OF MULTI-AGENT Q-LEARNING FOR COOPERATIVE TASK-PLANNING 107.

2.1 INTRODUCTION 108 -- 2.2 LITERATURE REVIEW 112 -- 2.3 PRELIMINARIES 114 -- 2.3.1 Single agent Q-learning 114 -- 2.3.2 Multi-agent Q-learning 115 -- 2.4 PROPOSED MULTI-AGENT Q-LEARNING 118 -- 2.4.1 Two useful properties 119 -- 2.5 PROPOSED FCMQL ALGORITHMS AND THEIR CONVERGENCE ANALYSIS 120 -- 2.5.1 Proposed FCMQL algorithms 120 -- 2.5.2 Convergence analysis of the proposed FCMQL algorithms 121 -- 2.6 FCMQL-BASED COOPERATIVE MULTI-AGENT PLANNING 122 -- 2.7 EXPERIMENTS AND RESULTS 123 -- 2.8 CONCLUSIONS 130 -- 2.9 SUMMARY 131 -- 2.10 APPENDIX 2.1 131 -- 2.11 APPENDIX 2.2 135 -- References 152 -- CHAPTER 3 CONSENSUS Q-LEARNING FOR MULTI-AGENT COOPERATIVE PLANNING 157 -- 3.1 INTRODUCTION 158 -- 3.2 PRELIMINARIES 159 -- 3.2.1 Single agent Q-learning 159 -- 3.2.2 Equilibrium-based multi-agent Q-learning 160 -- 3.3 CONSENSUS 161 -- 3.4 PROPOSED CONSENSUS Q-LEARNING AND PLANNING 162 -- 3.4.1 Consensus Q-learning 162 -- 3.4.2 Consensus-based multi-robot planning 164 -- 3.5 EXPERIMENTS AND RESULTS 165 -- 3.5.1 Experimental setup 165 -- 3.5.2 Experiments for CoQL 165 -- 3.5.3 Experiments for consensus-based planning 166 -- 3.6 CONCLUSIONS 168 -- 3.7 SUMMARY 168 -- References 168 -- CHAPTER 4 AN EFFICIENT COMPUTING OF CORRELATED EQUILIBRIUM FOR COOPERATIVE Q-LEARNING BASED MULTI-AGENT PLANNING 171 -- 4.1 INTRODUCTION 172 -- 4.2 SINGLE-AGENT Q-LEARNING AND EQUILIBRIUM BASED MAQL 175 -- 4.2.1 Single Agent Q learning 175 -- 4.2.2 Equilibrium based MAQL 175 -- 4.3 PROPOSED COOPERATIVE MULTI-AGENT Q-LEARNING AND PLANNING 176 -- 4.3.1 Proposed schemes with their applicability 176 -- 4.3.2 Immediate rewards in Scheme-I and -II 177 -- 4.3.3 Scheme-I induced MAQL 178 -- 4.3.4 Scheme-II induced MAQL 180 -- 4.3.5 Algorithms for scheme-I and II 182 -- 4.3.6 Constraint QL-I/ QL-II(C ......................................................... 183 -- 4.3.7 Convergence 183 -- Multi-agent planning 185 -- 4.4 COMPLEXITY ANALYSIS 186 -- 4.4.1 Complexity of Correlated Q-Learning 187 -- 4.4.1.1 Space Complexity 187.

4.4.1.2 Time Complexity 187 -- 4.4.2 Complexity of the proposed algorithms 188 -- 4.4.2.1 Space Complexity 188 -- 4.4.2.2 Time Complexity 188 -- 4.4.3 Complexity comparison 189 -- 4.4.3.1 Space complexity 190 -- 4.4.3.2 Time complexity 190 -- 4.5 SIMULATION AND EXPERIMENTAL RESULTS 191 -- 4.5.1 Experimental platform 191 -- 4.5.1.1 Simulation 191 -- 4.5.1.2 Hardware 192 -- 4.5.2 Experimental approach 192 -- 4.5.2.1 Learning phase 193 -- 4.5.2.2 Planning phase 193 -- 4.5.3 Experimental results 194 -- 4.6 CONCLUSION 201 -- 4.7 SUMMARY 202 -- 4.8 APPENDIX 203 -- References 209 -- CHAPTER 5 A MODIFIED IMPERIALIST COMPETITIVE ALGORITHM FOR MULTI-AGENT STICK- CARRYING APPLICATION 213 -- 5.1 INTRODUCTION 214 -- 5.2 PROBLEM FORMULATION FOR MULTI-ROBOT STICK-CARRYING 219 -- 5.3 PROPOSED HYBRID ALGORITHM 222 -- 5.3.1 An Overview of Imperialist Competitive Algorithm (ICA) 222 -- 5.3.1.1 Initialization 222 -- 5.3.1.2 Selection of Imperialists and Colonies 223 -- 5.3.1.3 Formation of Empires 223 -- 5.3.1.4 Assimilation of Colonies 223 -- 5.3.1.5 Revolution 224 -- 5.3.1.6 Imperialistic Competition 224 -- 5.3.1.6.1 Total Empire Power Evaluation 225 -- 5.3.1.6.2 Reassignment of Colonies and Removal of Empire 225 -- 5.3.1.6.3 Union of Empires 226 -- 5.4 AN OVERVIEW OF FIREFLY ALGORITHM (FA) 226 -- 5.4.1 Initialization 226 -- 5.4.2 Attraction to Brighter Fireflies 226 -- 5.4.3 Movement of Fireflies 227 -- 5.5 PROPOSED IMPERIALIST COMPETITIVE FIREFLY ALGORITHM 227 -- 5.5.1 Assimilation of Colonies 229 -- 5.5.1.1 Attraction to Powerful Colonies 230 -- 5.5.1.2 Modification of Empire Behavior 230 -- 5.5.1.3 Union of Empires 230 -- 5.6 SIMULATION RESULTS 232 -- 5.6.1 Comparative Framework 232 -- 5.6.2 Parameter Settings 232 -- 5.6.3 Analysis on Explorative Power of ICFA 232 -- 5.6.4 Comparison of Quality of the Final Solution 233 -- 5.6.5 Performance Analysis 233 -- 5.7 COMPUTER SIMULATION AND EXPERIMENT 240 -- 5.7.1 Average total path deviation (ATPD) 240 -- 5.7.2 Average Uncovered Target Distance (AUTD) 241.

5.7.3 Experimental Setup in Simulation Environment 241 -- 5.7.4 Experimental Results in Simulation Environment 242 -- 5.7.5 Experimental Setup with Khepera Robots 244 -- 5.7.6 Experimental Results with Khepera Robots 244 -- 5.8 CONCLUSION 245 -- 5.9 SUMMARY 247 -- 5.10 APPENDIX 5.1 248 -- References 249 -- CHAPTER 6 CONCLUSIONS AND FUTURE DIRECTIONS 255 -- 6.1 CONCLUSIONS 256 -- 6.2 FUTURE DIRECTIONS 257.

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"This book explores the usage of Reinforcement Learning for Multi-Agent Coordination. Chapter 1 introduces fundamentals of the multi-robot coordination. Chapter 2 offers two useful properties, which have been developed to speed-up the convergence of traditional multi-agent Q-learning (MAQL) algorithms in view of the team-goal exploration, where team-goal exploration refers to simultaneous exploration of individual goals. Chapter 3 proposes the novel consensus Q-learning (CoQL), which addresses the equilibrium selection problem. Chapter 4 introduces a new dimension in the literature of the traditional correlated Q-learning (CQL), in which correlated equilibrium (CE) is computed partly in the learning and the rest in the planning phases, thereby requiring CE computation once only. Chapter 5 proposes an alternative solution to the multi-agent planning problem using meta-heuristic optimization algorithms. Chapter 6 provides the concluding remarks based on the principles and experimental results acquired in the previous chapters. Possible future directions of research are also examined briefly at the end of the chapter."-- Provided by publisher.

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