Before revision:  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 .
After revision:  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 .