Multi-Agent Low-Dimensional Linear Bandits

TL;DR

This paper introduces a decentralized multi-agent linear bandit algorithm leveraging side information about low-dimensional subspaces, significantly reducing regret through collaboration and communication.

Contribution

It proposes a novel decentralized algorithm that enables agents to communicate subspace information, improving regret bounds in multi-agent linear bandit problems with side information.

Findings

Per-agent regret is significantly reduced with communication.

The algorithm effectively distributes subspace search among agents.

Simulations confirm improved performance over non-communicative approaches.

Abstract

We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector $\theta^* \in \mathbb{R}^d$. The side information consists of a finite collection of low-dimensional subspaces, one of which contains $\theta^*$. In our setting, agents can collaborate to reduce regret by sending recommendations across a communication graph connecting them. We present a novel decentralized algorithm, where agents communicate subspace indices with each other and each agent plays a projected variant of LinUCB on the corresponding (low-dimensional) subspace. By distributing the search for the optimal subspace across users and learning of the unknown vector by each agent in the corresponding low-dimensional subspace, we show that the per-agent finite-time regret is much smaller than the case when agents do not communicate. We finally complement these results through simulations.