Decentralized Heterogeneous Multi-Player Multi-Armed Bandits with Non-Zero Rewards on Collisions

We consider a fully decentralized multi-player stochastic multi-armed bandit setting where the players cannot communicate with each other and can observe only their own actions rewards. The environment may appear differently to different players, i.e., reward distributions for given arm are heterogeneous across players. In case of collision (when more than one player plays same arm), we allow colliding receive non-zero time-horizon T which arms played is not known Within this setup, number allowed be greater arms, present policy that achieves near order-optimal expected regret order O(log1+δ T) δ > 0 (however small) over duration T.