Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Path

Muhammad Aneeq uz Zaman, Alec Koppel, Sujay Bhatt, Tamer Başar

Research output: Contribution to journalConference articlepeer-review


We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the single sample path of the generic agent. We call this Sandbox Learning, as it can be used as a warm-start for any agent learning in a multi-agent non-cooperative setting. We adopt a two timescale approach in which an online fixed-point recursion for the mean-field operates on a slower time-scale, in tandem with a control policy update on a faster time-scale for the generic agent. Given that the underlying Markov Decision Process (MDP) of the agent is communicating, we provide finite sample convergence guarantees in terms of convergence of the mean-field and control policy to the mean-field equilibrium. The sample complexity of the Sandbox learning algorithm is O(ϵ−4) where ϵ is the MFE approximation error. This is similar to works which assume access to oracle. Finally, we empirically demonstrate the effectiveness of the sandbox learning algorithm in diverse scenarios, including those where the MDP does not necessarily have a single communicating class.

Original languageEnglish (US)
Pages (from-to)10178-10206
Number of pages29
JournalProceedings of Machine Learning Research
StatePublished - 2023
Externally publishedYes
Event26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain
Duration: Apr 25 2023Apr 27 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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