Behaviour Analysis of Mixed Game-Theoretic Learning Algorithms

Distributed optimisation becomes ever more important to boost the operational efficiency of autonomous systems. A number of algorithms have been proposed to solve distributed optimisation problems in recent years. A common assumption has been that these individual agents use the same type of learning algorithm. There are however applications such as reconfigurable robotics and a robotic team's coordination, where this assumption is not always valid. In this paper, we propose a methodology that allows the study of agents' joint behavior when they use different game-theoretic learning algorithms. Our methodology is based on probabilistic model checking, and we use a new a behaviour-similarity-relation to build compact state spaces. Our theory and computational procedures of formal verification provide a framework to study the properties of solutions. The proposed methodology is demonstrated on four learning algorithms that are used to solve five games that can be considered as distributed optimisation tasks.