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Game-Theoretic Learning and Distributed Optimization in Memoryless Multi-Agent Systems
This book presents new efficient methods for optimization in realistic large-scale, multi-agent systems. These methods do not require the agents to have the full information about the system, but instead allow them to make their local decisions based only on the local information, possibly obtained...
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint : Springer,
2017.
Cham : 2017. |
| Physical Description: |
1 online resource (IX, 171 pages 38 illustrations) : online resource. |
| Subjects: | |
| Online Access: | SpringerLink - Click here for access |
Contents:
- Abstract; Contents; 1 Introduction; 1.1 Motivation of Research; 1.2 List of Notations; 2 Game Theory and Multi-Agent Optimization; 2.1 Game Theory; 2.1.1 Introduction to Game Theory; 2.1.2 Nash Equilibrium; 2.1.3 Potential Games; 2.2 Potential Game Design in Multi-Agent Optimization; 2.2.1 Multi-Agent Systems Modeled by Means of Potential Games; 2.2.2 Learning Optimal States in Potential Games; 2.3 Distributed Optimization in Multi-Agent Systems; References; 3 Logit Dynamics in Potential Games with Memoryless Players; 3.1 Introduction.
- 3.2 Memoryless Learning in Discrete Action Games as a Regular Perturbed Markov Chain3.2.1 Preliminaries: Regular Perturbed Markov Chains; 3.2.2 Convergence in Total Variation of General Memoryless Learning Algorithms; 3.3 Asynchronous Learning; 3.3.1 Log-Linear Learning in Discrete Action Games; 3.3.1.1 An Example: Log-Linear Learning for Consensus Problem; 3.3.2 Convergence to Potential Function Maximizers; 3.4 Synchronization in Memoryless Learning; 3.4.1 Additional Information is Needed; 3.4.2 Independent Log-Linear Learning in Discrete Action Games.
- 3.4.3 Convergence to Potential Function Maximizers3.5 Convergence Rate Estimation and Finite Time Behavior; 3.5.1 Convergence Rate of Time-Inhomogeneous Log-Linear Learning; 3.5.2 Convergence Rate of Time-Inhomogeneous Independent Log-Linear Learning; 3.5.3 Simulation Results: Example of a SensorCoverage Problem; 3.5.3.1 Inhomogeneous Log-Linear Learning in Coverage Problem; 3.5.3.2 Inhomogeneous Independent Log-Linear Learning in Coverage Problem; 3.6 Learning in Continuous Action Games; 3.6.1 Log-Linear Learning in Continuous Action Games.
- 4.3 Push-Sum Algorithm in Non-convex Distributed Optimization4.3.1 Problem Formulation: Push-Sum Algorithm and Assumptions; 4.3.2 Convergence to Critical Points; 4.3.3 Perturbed Procedure: Convergence to Local Minima; 4.3.4 Convergence Rate of the Perturbed Process; 4.3.5 Simulation Results: Illustrative Example and Congestion Routing Problem; 4.4 Communication-Based Memoryless Learningin Potential Games; 4.4.1 Simulation Results: Code Division Multiple Access Problem; 4.5 Payoff-Based Learning in Potential Games; 4.5.1 Convergence to a Local Maximum of the PotentialFunction.