Learning in Distributed Contextual Linear Bandits Without Sharing the Context
This addresses communication bottlenecks in distributed systems like wireless applications, offering incremental improvements in efficiency for specific scenarios.
The paper tackles the problem of distributed contextual linear bandits where agents observe contexts but are separated from the learner, proposing a method that uses about 5d bits per context for unknown distributions or 0 bits for known distributions, achieving nearly the same regret as if contexts were directly observable, with improvements like eliminating a log(T) factor.
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.