  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.
