Restless Multi-Armed Bandits under Exogenous Global Markov Process

TL;DR

This paper introduces the LEMP algorithm for restless multi-armed bandits influenced by an unknown exogenous Markov process, achieving logarithmic regret bounds and outperforming existing methods.

Contribution

The paper proposes the LEMP algorithm tailored for RMAB problems with unknown exogenous Markov influences, providing theoretical regret bounds and empirical validation.

Findings

LEMP achieves logarithmic regret over time.

LEMP outperforms alternative algorithms in simulations.

Theoretical analysis confirms finite-sample regret bounds.

Abstract

We consider an extension to the restless multi-armed bandit (RMAB) problem with unknown arm dynamics, where an unknown exogenous global Markov process governs the rewards distribution of each arm. Under each global state, the rewards process of each arm evolves according to an unknown Markovian rule, which is non-identical among different arms. At each time, a player chooses an arm out of N arms to play, and receives a random reward from a finite set of reward states. The arms are restless, that is, their local state evolves regardless of the player's actions. Motivated by recent studies on related RMAB settings, the regret is defined as the reward loss with respect to a player that knows the dynamics of the problem, and plays at each time t the arm that maximizes the expected immediate value. The objective is to develop an arm-selection policy that minimizes the regret. To that end, we develop the Learning under Exogenous Markov Process (LEMP) algorithm. We analyze LEMP theoretically and establish a finite-sample bound on the regret. We show that LEMP achieves a logarithmic regret order with time. We further analyze LEMP numerically and present simulation results that support the theoretical findings and demonstrate that LEMP significantly outperforms alternative algorithms.