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Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning

Cui, Kai and Koeppl, Heinz (2021):
Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning.
24th International Conference on Artificial Intelligence and Statistics, Virtual Conference, 13.-15.04.2021, [Conference or Workshop Item]

Abstract

The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We show that all discrete-time finite MFGs with non-constant fixed point operators fail to be contractive as typically assumed in existing MFG literature, barring convergence via fixed point iteration. Instead, we incorporate entropy-regularization and Boltzmann policies into the fixed point iteration. As a result, we obtain provable convergence to approximate fixed points where existing methods fail, and reach the original goal of approximate Nash equilibria. All proposed methods are evaluated with respect to their exploitability, on both instructive examples with tractable exact solutions and high-dimensional problems where exact methods become intractable. In high-dimensional scenarios, we apply established deep reinforcement learning methods and empirically combine fictitious play with our approximations.

Item Type: Conference or Workshop Item
Erschienen: 2021
Creators: Cui, Kai and Koeppl, Heinz
Title: Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning
Language: English
Abstract:

The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We show that all discrete-time finite MFGs with non-constant fixed point operators fail to be contractive as typically assumed in existing MFG literature, barring convergence via fixed point iteration. Instead, we incorporate entropy-regularization and Boltzmann policies into the fixed point iteration. As a result, we obtain provable convergence to approximate fixed points where existing methods fail, and reach the original goal of approximate Nash equilibria. All proposed methods are evaluated with respect to their exploitability, on both instructive examples with tractable exact solutions and high-dimensional problems where exact methods become intractable. In high-dimensional scenarios, we apply established deep reinforcement learning methods and empirically combine fictitious play with our approximations.

Uncontrolled Keywords: 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
LOEWE
LOEWE > LOEWE-Zentren
LOEWE > LOEWE-Zentren > emergenCITY
TU-Projects: HMWK|III L6-519/03/05.001-(0016)|emergenCity TP Bock
Event Title: 24th International Conference on Artificial Intelligence and Statistics
Event Location: Virtual Conference
Event Dates: 13.-15.04.2021
Date Deposited: 22 Feb 2021 07:28
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