# Restless Multi-Armed Bandits under Exogenous Global Markov Process

arXiv: https://arxiv.org/abs/2202.13665 · HTML: https://mlsanity.com/paper/2202.13665/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 65 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Federated Learning: A Signal Processing Perspective](https://mlsanity.com/paper/2103.17150/) (2021)
- [Learning in Restless Multi-Armed Bandits via Adaptive Arm Sequencing Rules](https://mlsanity.com/paper/1906.08120/) (2019)
- [Distributed Learning over Markovian Fading Channels for Stable Spectrum Access](https://mlsanity.com/paper/2101.11292/) (2021)
- [On Sequential Elimination Algorithms for Best-Arm Identification in Multi-Armed Bandits](https://mlsanity.com/paper/1609.02606/) (2016)
- [Learning in Restless Bandits under Exogenous Global Markov Process](https://mlsanity.com/paper/2112.09484/) (2021)
- [An order optimal policy for exploiting idle spectrum in cognitive radio networks](https://mlsanity.com/paper/1709.00237/) (2017)
- [Learning to Detect an Odd Restless Markov Arm with a Trembling Hand](https://mlsanity.com/paper/2105.03603/) (2021)

## Built on by (most cited first, 4 of 4)

- [Context in Public Health for Underserved Communities: A Bayesian Approach to Online Restless Bandits](https://mlsanity.com/paper/2402.04933/) (2024)
- [Multi-Armed Bandits with Self-Information Rewards](https://mlsanity.com/paper/2209.02211/) (2022)
- [MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment](https://mlsanity.com/paper/2511.09324/) (2025)
- [Meta-Learning Multi-armed Bandits for Beam Tracking in 5G and 6G Networks](https://mlsanity.com/paper/2512.05680/) (2025)

## Abstract (arXiv)

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.