On Optimality of Myopic Policy for Restless Multi-armed Bandit Problem with Non i.i.d. Arms and Imperfect Detection
arXiv:1205.5375 · doi:10.1109/TSP.2011.2170684
Abstract
We consider the channel access problem in a multi-channel opportunistic communication system with imperfect channel sensing, where the state of each channel evolves as a non independent and identically distributed Markov process. This problem can be cast into a restless multi-armed bandit (RMAB) problem that is intractable for its exponential computation complexity. A natural alternative is to consider the easily implementable myopic policy that maximizes the immediate reward but ignores the impact of the current strategy on the future reward. In particular, we develop three axioms characterizing a family of generic and practically important functions termed as -regular functions which includes a wide spectrum of utility functions in engineering. By pursuing a mathematical analysis based on the axioms, we establish a set of closed-form structural conditions for the optimality of myopic policy.
Second version, 16 pages
References in corpus (3)
- On Myopic Sensing for Multi-Channel Opportunistic Access: Structure, Optimality, and Performance
- On the Optimality of Myopic Sensing in Multi-channel Opportunistic Access: the Case of Sensing Multiple Channels
- On Optimality of Myopic Sensing Policy with Imperfect Sensing in Multi-channel Opportunistic Access
Cited by in corpus (8)
- On Sequential Elimination Algorithms for Best-Arm Identification in Multi-Armed Bandits
- Task Offloading for Large-Scale Asynchronous Mobile Edge Computing: An Index Policy Approach
- Markovian restless bandits and index policies: A review
- Learning in Restless Bandits under Exogenous Global Markov Process
- On Optimality of Myopic Sensing Policy with Imperfect Sensing in Multi-channel Opportunistic Access
- Sufficient Conditions on the Optimality of Myopic Sensing in Opportunistic Channel Access: A Unifying Framework
- Minimax Optimal Algorithms for Adversarial Bandit Problem with Multiple Plays
- Optimality of Myopic Policy for Restless Multiarmed Bandit with Imperfect Observation