# Fairness for Workers Who Pull the Arms: An Index Based Policy for Allocation of Restless Bandit Tasks

arXiv: https://arxiv.org/abs/2303.00799 · HTML: https://mlsanity.com/paper/2303.00799/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [Fairness in Learning: Classic and Contextual Bandits](https://mlsanity.com/paper/1605.07139/) (2016)
- [Achieving Fairness in the Stochastic Multi-armed Bandit Problem](https://mlsanity.com/paper/1907.10516/) (2019)
- [Collapsing Bandits and Their Application to Public Health Interventions](https://mlsanity.com/paper/2007.04432/) (2020)
- [Field Study in Deploying Restless Multi-Armed Bandits: Assisting Non-Profits in Improving Maternal and Child Health](https://mlsanity.com/paper/2109.08075/) (2021)
- [Fair Contextual Multi-Armed Bandits: Theory and Experiments](https://mlsanity.com/paper/1912.08055/) (2019)
- [Planning to Fairly Allocate: Probabilistic Fairness in the Restless Bandit Setting](https://mlsanity.com/paper/2106.07677/) (2021)
- [Fair Division Under Cardinality Constraints](https://mlsanity.com/paper/1804.09521/) (2018)
- [Simulation Based Algorithms for Markov Decision Processes and Multi-Action Restless Bandits](https://mlsanity.com/paper/2007.12933/) (2020)

## Built on by (most cited first, 3 of 3)

- [Online Restless Multi-Armed Bandits with Long-Term Fairness Constraints](https://mlsanity.com/paper/2312.10303/) (2023)
- [Fairness and Privacy Guarantees in Federated Contextual Bandits](https://mlsanity.com/paper/2402.03531/) (2024)
- [Outcome-Fair Restless Multi-Armed Bandits for Stochastic Deadline Scheduling](https://mlsanity.com/paper/2607.23772/) (2026)

## Abstract (arXiv)

Motivated by applications such as machine repair, project monitoring, and anti-poaching patrol scheduling, we study intervention planning of stochastic processes under resource constraints. This planning problem has previously been modeled as restless multi-armed bandits (RMAB), where each arm is an intervention-dependent Markov Decision Process. However, the existing literature assumes all intervention resources belong to a single uniform pool, limiting their applicability to real-world settings where interventions are carried out by a set of workers, each with their own costs, budgets, and intervention effects. In this work, we consider a novel RMAB setting, called multi-worker restless bandits (MWRMAB) with heterogeneous workers. The goal is to plan an intervention schedule that maximizes the expected reward while satisfying budget constraints on each worker as well as fairness in terms of the load assigned to each worker. Our contributions are two-fold: (1) we provide a multi-worker extension of the Whittle index to tackle heterogeneous costs and per-worker budget and (2) we develop an index-based scheduling policy to achieve fairness. Further, we evaluate our method on various cost structures and show that our method significantly outperforms other baselines in terms of fairness without sacrificing much in reward accumulated.