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

TL;DR

This paper introduces a novel multi-worker restless bandit model that incorporates fairness and heterogeneous costs, extending the Whittle index approach to optimize intervention scheduling across multiple workers.

Contribution

It develops a multi-worker extension of the Whittle index and proposes an index-based policy to ensure fairness in resource allocation among heterogeneous workers.

Findings

Outperforms baseline methods in fairness metrics.

Maintains high reward levels despite fairness constraints.

Effective across various cost structures.

Abstract

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.