On Optimality of Myopic Policy for Restless MultiArmed Bandit Problem: An Axiomatic Approach
Abstract
We consider the channel access problem in a multichannel 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 multiarmed 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 $g$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 closedform structural conditions for the optimality of myopic policy.
 Publication:

IEEE Transactions on Signal Processing
 Pub Date:
 January 2012
 DOI:
 10.1109/TSP.2011.2170684
 arXiv:
 arXiv:1205.5375
 Bibcode:
 2012ITSP...60..300W
 Keywords:

 Computer Science  Systems and Control;
 Computer Science  Computer Science and Game Theory;
 94A05;
 C.2.1;
 G.1.6
 EPrint:
 Second version, 16 pages