Model predictive control is almost optimal for restless bandits

Dheeraj Narasimha, Nicolas Gast

Keywords: Restless Multi-Armed Bandits, Markov Decision Processes, Constrained Optimization, Stochastic Control

TL;DR: Simple model predictive control is "almost" good enough to solve the long standing Restless Multi-Armed Bandit Problem under minimal assumptions

Abstract: We consider the discrete time infinite horizon average reward restless markovian bandit (RMAB) problem. We propose a model predictive control based non-stationary policy with a rolling computational horizon $\tau$. At each time-slot, this policy solves a $\tau$ horizon linear program whose first control value is kept as a control for the RMAB. Our solution requires minimal assumptions and quantifies the loss in optimality in terms of $\tau$ and the number of arms, $N$. We show that its sub-optimality gap is $O(1/\sqrt{N})$ in general, and $\exp(-\Omega{N})$ under a local-stability condition. Our proof is based on a framework from dynamic control known as dissipativity. Not only is our solution easy to implement but performs very well in practice when compared to the state of the art. Further, both our solution and our proof methodology can easily be generalized to more general constrained MDP settings and should thus, be of great interest to the burgeoning RMAB community.

Primary Area: learning on time series and dynamical systems

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Submission Number: 5076