Decentralized Restless Bandit with Multiple Players and Unknown Dynamics

We consider decentralized restless multi-armed bandit problems with unknown dynamics and multiple players. The reward state of each arm transits according to an unknown Markovian rule when it is played and evolves according to an arbitrary unknown random process when it is passive. Players activating the same arm at the same time collide and suffer from reward loss. The objective is to maximize the long-term reward by designing a decentralized arm selection policy to address unknown reward models and collisions among players. A decentralized policy is constructed that achieves a regret with logarithmic order when an arbitrary nontrivial bound on certain system parameters is known. When no knowledge about the system is available, we extend the policy to achieve a regret arbitrarily close to the logarithmic order. The result finds applications in communication networks, financial investment, and industrial engineering.