Efficient Reinforcement Learning for Global Decision Making in the Presence of Local Agents at Scale

Emile Timothy Anand, Guannan Qu

Keywords: Reinforcement Learning, Multi-agent Systems, Large-scale Systems, Mean-field Approximation

TL;DR: We develop a scalable algorithm for global decision-making in the presence of many local agents, where the global decision-maker samples local agents to make decisions to maximize the system rewards, therefore overcoming the curse of dimensionality.

Abstract:

We study reinforcement learning for global decision-making in the presence of local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the joint rewards of all the agents. Such problems find many applications, e.g. demand response, EV charging, and queueing. In this setting, scalability has been a long-standing challenge due to the size of the joint state space which can be exponential in the number of agents. This work proposes the \texttt{SUBSAMPLE-Q} algorithm, where the global agent subsamples $k\leq n$ local agents to compute a policy in time that is polynomial in $k$. We show that this learned policy converges to the optimal policy on the order of $\tilde{O}(1/\sqrt{k}+\epsilon_{k,m})$ as the number of subsampled agents $k$ increases, where ${\epsilon}_{k,m}$ is the Bellman noise. Finally, we validate our theoretical results through numerical simulations in demand-response and queueing settings.

Primary Area: reinforcement learning

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Submission Number: 11550