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Abstract

The present thesis considers two biologically significant processes: the evolution of populations of organisms through natural selection and the change of individual behaviour through learning. More specifically, we consider evolution and learning as guided by the interactions of multiple populations or of multiple learners, respectively, where we assume that these interactions can be described in the language of game theory. While the evolution of populations is often considered in the framework of evolutionary game theory and learning is often considered in the framework of multi-agent reinforcement learning, this thesis strives to present a common perspective on these two classes of processes by analysing the relation between the multi population replicator dynamics of evolutionary games and simple multi-agent reinforcement learning algorithms.

In particular, this thesis addresses the question of when such processes lead a system of interest, be it populations of organisms or individual learners, to states which reflect the game theoretic structure describing the interactions between populations or between individuals, respectively, and specifically when such systems converge to the Nash equilibria of the underlying game. We motivate these ideas by considering a preliminary application to learning in artificial neural networks, as a concrete multi-agent learning setting of high interest in the fields of artificial intelligence and machine learning. We address the challenges to obtain convergence to interior Nash equilibria in multi-population replicator dynamics by considering more closely the effects of weak mutation. In order to more explicitly account for mutation we specify a replicator-mutator dynamics and relate the equilibria of these dynamics to the underlying game’s Nash equilibria in a precise manner, showing that this relation is independent of the choice of mutation parameters. We further prove that such mutation stabilises Nash equilibria in two-player zero-sum games. Finally, we demonstrate how our results regarding the replicator-mutator dynamics can inform the formulation of concrete multi-agent learning algorithms and provide an analytical investigation of the convergence properties of such a learning algorithm.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	Doctoral Theses School of Science & Technology > School of Science & Technology Doctoral Theses School of Science & Technology > Mathematics

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