Coordination without communication: optimal regret in two players multi-armed bandits

We consider two agents playing simultaneously the same stochastic three-armed bandit problem. The two agents are cooperating but they cannot communicate. We propose a strategy with no collisions at all between the players (with very high probability), and with near-optimal regret O(√T log(T)). We also argue that the extra logarithmic term √log(T) should be necessary by proving a lower bound for a full information variant of the problem.