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 .
After revision:  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 regret is much smaller than the case when agents do not communicate .