Natural gradient in evolutionary games

Date: Tue. October 18, 2022
Event: FAU DCN-AvH Seminar
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: FAU DCN-AvH Seminar “Natural gradient in evolutionary games”

Speaker: Prof. Dr. Vladimir Jaćimović
Affiliation: Faculty of Natural Sciences and Mathematics, University of Montenegro

Abstract. I will start with a very brief overview of optimization methods. These methods are divided into gradient-based techniques (such as gradient descent) and gradient- free algorithms (stochastic search and evolutionary algorithms).

In the second part, I will explain the setup of an evolutionary game and intro- duce replicator equations. Evolutionary Game Theory has been founded in 1970’s as a subfield of Game Theory, inspired by the Darwinian principles. I will demon- strate that evolutionary dynamics can be interpreted a process of collective learning, during which a certain function is maximized over the family of probability distribu- tions. Evolutionary dynamics generate an iterative method for maximization of this objective function. Based on the information-geometric approach to evolutionary dynamics, I answer the following questions:
a) What is the objective that the population during an evolutionary game tends to maximize?
b) How individuals, by following their simple rules, (unknowingly) contribute to the achievement of this collective objective?

Finally, we will briefly comment on recent applications of these paradigms and algorithms in Artificial Intelligence.