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Learning Graphon Mean Field Games and Approximate Nash Equilibria

Cui, K. ; Koeppl, H. (2022)
Learning Graphon Mean Field Games and Approximate Nash Equilibria.
10th International Conference on Learning Representations (ICLR 2022). virtual Conference (25.-29.04.2022)
Conference or Workshop Item, Bibliographie

Abstract

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely limited to graphon mean field systems with continuous-time diffusive or jump dynamics, typically without control and with little focus on computational methods. We propose a novel discrete-time formulation for graphon mean field games as the limit of non-linear dense graph Markov games with weak interaction. On the theoretical side, we give extensive and rigorous existence and approximation properties of the graphon mean field solution in sufficiently large systems. On the practical side, we provide general learning schemes for graphon mean field equilibria by either introducing agent equivalence classes or reformulating the graphon mean field system as a classical mean field system. By repeatedly finding a regularized optimal control solution and its generated mean field, we successfully obtain plausible approximate Nash equilibria in otherwise infeasible large dense graph games with many agents. Empirically, we are able to demonstrate on a number of examples that the finite-agent behavior comes increasingly close to the mean field behavior for our computed equilibria as the graph or system size grows, verifying our theory. More generally, we successfully apply policy gradient reinforcement learning in conjunction with sequential Monte Carlo methods.

Item Type: Conference or Workshop Item
Erschienen: 2022
Creators: Cui, K. ; Koeppl, H.
Type of entry: Bibliographie
Title: Learning Graphon Mean Field Games and Approximate Nash Equilibria
Language: English
Date: April 2022
Event Title: 10th International Conference on Learning Representations (ICLR 2022)
Event Location: virtual Conference
Event Dates: 25.-29.04.2022
Corresponding Links:
Abstract:

Recent advances at the intersection of dense large graph limits and mean field games have begun to enable the scalable analysis of a broad class of dynamical sequential games with large numbers of agents. So far, results have been largely limited to graphon mean field systems with continuous-time diffusive or jump dynamics, typically without control and with little focus on computational methods. We propose a novel discrete-time formulation for graphon mean field games as the limit of non-linear dense graph Markov games with weak interaction. On the theoretical side, we give extensive and rigorous existence and approximation properties of the graphon mean field solution in sufficiently large systems. On the practical side, we provide general learning schemes for graphon mean field equilibria by either introducing agent equivalence classes or reformulating the graphon mean field system as a classical mean field system. By repeatedly finding a regularized optimal control solution and its generated mean field, we successfully obtain plausible approximate Nash equilibria in otherwise infeasible large dense graph games with many agents. Empirically, we are able to demonstrate on a number of examples that the finite-agent behavior comes increasingly close to the mean field behavior for our computed equilibria as the graph or system size grows, verifying our theory. More generally, we successfully apply policy gradient reinforcement learning in conjunction with sequential Monte Carlo methods.

Uncontrolled Keywords: Computer Science and Game Theory; Machine Learning; Multiagent Systems; Optimization and Control; emergenCity_KOM; emergenCITY_KOM
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
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LOEWE > LOEWE-Zentren
LOEWE > LOEWE-Zentren > emergenCITY
Date Deposited: 01 Feb 2022 07:33
Last Modified: 06 Sep 2022 08:32
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