Multi-Agent Low-Dimensional Linear Bandits
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We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector θ^* ∈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. Through a combination of collaborative best subspace identification, and per-agent learning of an unknown vector in the corresponding low-dimensional subspace, we show that the per-agent regret is much smaller than the case when agents do not communicate. By collaborating to identify the subspace containing θ^*, we show that each agent effectively solves an easier instance of the linear bandit (compared to the case of no collaboration), thus leading to the reduced per-agent regret. We finally complement these results through simulations.
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