An Index Policy for Minimizing the Uncertainty-of-Information of Markov Sources

TL;DR

This paper develops an index policy for scheduling Markov sources to minimize the uncertainty-of-information, measured by Shannon entropy, using a relaxed restless multi-armed bandit approach and a gradient-based solution.

Contribution

It introduces a universal index policy for RMABs that minimizes the uncertainty-of-information in Markov sources, extending existing methods to a broader class of problems.

Findings

The index policy effectively minimizes the sum-UoI in Markov sources.

The relaxed problem reduces to maximizing a concave, piecewise linear function.

The proposed method is applicable to general RMABs with bounded costs.

Abstract

This paper focuses on the information freshness of finite-state Markov sources, using the uncertainty of information (UoI) as the performance metric. Measured by Shannon's entropy, UoI can capture not only the transition dynamics of the Markov source but also the different evolutions of information quality caused by the different values of the last observation. We consider an information update system with M finite-state Markov sources transmitting information to a remote monitor via m communication channels. Our goal is to explore the optimal scheduling policy to minimize the sum-UoI of the Markov sources. The problem is formulated as a restless multi-armed bandit (RMAB). We relax the RMAB and then decouple the relaxed problem into M single bandit problems. Analyzing the single bandit problem provides useful properties with which the relaxed problem reduces to maximizing a concave and piecewise linear function, allowing us to develop a gradient method to solve the relaxed problem and obtain its optimal policy. By rounding up the optimal policy for the relaxed problem, we obtain an index policy for the original RMAB problem. Notably, the proposed index policy is universal in the sense that it applies to general RMABs with bounded cost functions.