Multi-player Multi-Armed Bandits with non-zero rewards on collisions for uncoordinated spectrum access

In this paper, we study the uncoordinated spectrum access problem using the multi-player multi-armed bandits framework. We consider a model where there is no central control and the users cannot communicate with each other. The environment may appear differently to different users, \textit{i.e.}, the mean rewards as seen by different users for a particular channel may be different. Additionally, in case of a collision, we allow for the colliding users to receive non-zero rewards. With this setup, we present a policy that achieves expected regret of order $O(\log^{2+\delta}{T})$ for some $\delta > 0$.