Learning in A Changing World: Non-Bayesian Restless Multi-Armed Bandit

We consider the restless multi-armed bandit (RMAB) problem with unknown dynamics. In this problem, at each time, a player chooses K out of N (N > K) arms to play. The state of each arm determines the reward when the arm is played and transits according to Markovian rules no matter the arm is engaged or passive. The Markovian dynamics of the arms are unknown to the player. The objective is to maximize the long-term reward by designing an optimal arm selection policy. The performance of a policy is measured by regret, defined as the reward loss with respect to the case where the player knows which K arms are the most rewarding and always plays these K best arms. We construct a policy, referred to as Restless Upper Confidence Bound (RUCB), that achieves a regret with logarithmic order of time when an arbitrary nontrivial bound on certain system parameters is known. When no knowledge about the system is available, we extend the RUCB policy to achieve a regret arbitrarily close to the l...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Haoyang Liu, Keqin Liu, Qing Zhao
• Keywords: Arm Selection Policy, CORR 2010, Education, Logarithmic Order, Restless Multi-armed Bandit