Abstract: Understanding how large groups of agents interact is critical in fields like economics, finance, and engineering. However, directly analyzing $N$-player games becomes infeasible as the number of agents grows. Mean-field games (MFGs) provide a powerful solution by approximating these complex systems, allowing us to study the collective behavior of a large population as the limit of the $N$-player game when $N$ is very large. This approximation significantly simplifies analysis while retaining key insights about the system.

In this talk, we present recent advancements at the intersection of MFGs and multi-agent reinforcement learning (MARL). First, we introduce Mean-Field Occupation Measure Optimization (MF-OMO), a novel framework that reinterprets Nash equilibria in discrete-time MFGs as a single optimization problem over occupation measures. This reformulation avoids restrictive assumptions often required by traditional methods and enables the use of standard optimization algorithms to find multiple equilibria. We also extend this approach to continuous-time finite-state MFGs, broadening its applicability.

Building on the concept of occupation measures, we then propose Mean-Field Occupation Measure Learning (MF-OML), the first fully polynomial online reinforcement learning algorithm capable of finding approximate Nash equilibria in large population games beyond variants of zero-sum and potential games. We establish regret bounds for the $N$-player games that can be approximated by MFGs under monotonicity conditions. 

Together, these advancements provide a comprehensive approach to characterizing and solving Nash equilibria in complex multi-agent environments.

Short bio:  Anran Hu is an assistant professor at Columbia University, working at the intersection of stochastic control, game theory, optimization, and machine learning. Her research focuses on mean-field games, continuous-time stochastic control, and reinforcement learning, spanning the full spectrum from fundamentally new frameworks, analytical theory, efficient algorithms to open-source software for such problems which have wide applications in finance, economy, transportation, robotics and energy systems. Before joining Columbia, she was a Hooke Research Fellow at the University of Oxford and earned her Ph.D. from Berkeley IEOR and her B.S. from Peking University.

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