Multi-Agent Low-Dimensional Linear Bandits
This work addresses the challenge of efficient collaboration in multi-agent bandit systems, which is incremental as it builds on existing linear bandit methods by incorporating decentralized communication.
The paper tackles the problem of multi-agent stochastic linear bandits with side information, where agents collaborate via communication to reduce regret by searching for an optimal low-dimensional subspace, resulting in significantly smaller per-agent regret compared to non-communicating agents.
We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector $θ^* \in \mathbb{R}^d$. The side information consists of a finite collection of low-dimensional subspaces, one of which contains $θ^*$. 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.