Game theoretic approaches to motion planning in robot soccer / Marcus Post. 2008
Content
Introduction
Reinforcement Learning (RL) and Game Theory
Dynamical Systems and Markov Processes
Markov Decision Processes (MDPs)
Matrix Games
Two Player Zero Sum Markov Games (2P-ZS-MGs)
General Markov Games, Differential Games, and Advanced Concepts of RL
Model Reduction and Symmetry
Supervised Learning (SL), Function Approximation, Generalisation
Introduction
General Approximation Results
Generalisation
Function Approximation with Automated Basis Determination
Value Iteration with SL: Convergence Result
Combination of RL and SL: Practical Results from Literature
Robot Soccer and Other Applications
Modeling Robot Soccer
Numerical Results of Grid Soccer
Preliminaries for the Following Subsections
Reasoning for 2P-ZS-MG Modelling: Comparison of MDP and 2P-ZS-MG strategies
Relating Policies to Humanoid Soccer Characteristics
Comparison of DP and RL Techniques
Comparison of Different DP Techniques with Various Parameters
Comparison of Standard Methods and SL Techniques
Towards Multi-Player Robot Soccer: 2v2 Grid Soccer
A New Algorithm: MaG-Clus-VI
From Grid Soccer to Robot Soccer: Practical Issues
Other Applications
Conclusion and Outlook
Basics of Group Homomorphisms and Group Actions
Bellman Equations and Iterative Linear Solvers
The Software Package DRPOST
Detailed Tables of Numerical Results
Initial Value Functions [0] and Discount Factors
Additional Figures and Tables for the Comparative Studies of DP and RL methods
List of Figures
List of Tables
Glossary
Bibliography
Index