Learning in Distributed Contextual Linear Bandits Without Sharing the Context

TL;DR

This paper introduces a communication-efficient distributed learning method for contextual linear bandits that minimizes context sharing while maintaining near-optimal regret, applicable in wireless settings with large feature spaces.

Contribution

It proposes a novel approach that reduces context communication to approximately 5d bits or zero bits with known distribution, achieving near-optimal regret bounds.

Findings

Reduces context communication to ~5d bits per context

Achieves regret bounds close to fully observable contexts

Improves upon existing bounds by a logarithmic factor

Abstract

Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance bottleneck, especially when the contexts come from a large $d$-dimensional space. In this paper, we consider a distributed memoryless contextual linear bandit learning problem, where the agents who observe the contexts and take actions are geographically separated from the learner who performs the learning while not seeing the contexts. We assume that contexts are generated from a distribution and propose a method that uses $\approx 5d$ bits per context for the case of unknown context distribution and $0$ bits per context if the context distribution is known, while achieving nearly the same regret bound as if the contexts were directly observable. The former bound improves upon existing bounds by a $\log(T)$ factor, where $T$ is the length of the horizon, while the latter achieves information theoretical tightness.