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 and rewards. The environment may appear differently to different players,
$\textit {i.e.}$
, the reward distributions for a given arm are heterogeneous across players. In the case of a collision (when more than one player plays the same arm), we allow for the colliding players to receive non-zero rewards. The time-horizon
$T$
for which the arms are played is
not
known to the players. Within this setup, where the number of players is allowed to be greater than the number of arms, we present a policy that achieves near order-optimal expected regret of order
$O(\log ^{1 + \delta } T)$
for
$\delta >0$
(however small) over a time-horizon of duration
$T$
.