Stochastic Bandits for Egalitarian Assignment

TL;DR

This paper introduces EgalMAB, a stochastic multi-armed bandit problem focused on fair user-arm assignments, proposing a UCB-based solution and analyzing its regret bounds alongside an impossibility result.

Contribution

It formulates the EgalMAB problem, develops the EgalUCB policy, and provides theoretical regret bounds and impossibility results for fair assignment in stochastic bandits.

Findings

EgalUCB achieves sublinear regret bounds.

An impossibility result shows limitations of fair assignment policies.

The approach applies to fairness in resource allocation.

Abstract

We study EgalMAB, an egalitarian assignment problem in the context of stochastic multi-armed bandits. In EgalMAB, an agent is tasked with assigning a set of users to arms. At each time step, the agent must assign exactly one arm to each user such that no two users are assigned to the same arm. Subsequently, each user obtains a reward drawn from the unknown reward distribution associated with its assigned arm. The agent's objective is to maximize the minimum expected cumulative reward among all users over a fixed horizon. This problem has applications in areas such as fairness in job and resource allocations, among others. We design and analyze a UCB-based policy EgalUCB and establish upper bounds on the cumulative regret. In complement, we establish an almost-matching policy-independent impossibility result.