We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector \theta^* \in 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. 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 \theta^*, 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.
We study a multi-agent stochastic linear bandit with side information, parameterized by an unknown vector \theta^* \in 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.
D
,
R
Through a combination of collaborative best subspace identification, and per-agent learning of an unknown vector
By distributing the search for the optimal subspace across users and learning of the unknown vector by each agent
A
finite-time
D
. By collaborating to identify the subspace containing \theta^*, 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