Decision making in multi-agent systems arises in applications ranging from online auctions and markets to telecommunication and transportation networks. Game theory provides a powerful framework for analyzing and optimizing decisions in multi-agent systems. The notion of an equilibrium in a game characterizes stable solutions to multi-agent decision making problems.
The objective of this project is to explore distributed learning algorithms to converge to Nash equilibria in a class of convex games.
In many practical situations the agents do not know functional form of their objectives and can only access the values of their objective functions at a played action. Such situations arise, for example, in electricity markets (unknown price functions or constraints), network routing (unknown traffic demands/constraints), and sensor coverage problems (unknown density function on the mission space). Hence, from the perspective of each player, she can only has access to blackbox information of her objective function. In this project, we explore algorithms that use only blackbox information. The student will explore the class of mirror-descent zero-order algorithms for learning Nash equilibria. She/he will implement several algorithms in this class for a set of standard games. She will benchmark their performance. She will quantify and compare their convergence rate in
simulation. The student will advance the theory to characterize the convergence rate in terms of the properties of the underlying game.
This work requires strong background in probability, convex optimization and basics of game theory, such as Nash equilibrium. The student will develop theoretical skills in understanding underpinning of a large class of learning algorithms. She will develop theoretical skills by extending their analysis. She will also develop coding skills by implementing and benchmarking the algorithms. There is possibility of doing this as a semester or a Master’s project. To determine if you have interest, you may read the following paper and check out some of its references:
https://arxiv.org/pdf/2202.11147.pdf
To apply, send an email containing 1. one paragraph on your background and fit for the project, 2. your BS and MS transcripts to [email protected].
The students who have suitable
track record will be contacted.