Optimal Sampling for Uncertainty-of-Information Minimization in a Remote Monitoring System

TL;DR

This paper develops optimal sampling strategies for remote binary source monitoring over delayed channels using uncertainty of information, extending previous models to include random delays and proposing efficient algorithms.

Contribution

It introduces a POMDP-based framework with belief states for UoI minimization under random delays and presents both optimal and sub-optimal algorithms for policy computation.

Findings

Sampling policies outperform traditional zero wait and AoI-based policies.

The sub-optimal index-based policy nearly matches the optimal policy's performance.

Policies are especially effective under large delay conditions.

Abstract

In this paper, we study a remote monitoring system where a receiver observes a remote binary Markov source and decides whether to sample and transmit the state through a randomly delayed channel. We adopt uncertainty of information (UoI), defined as the entropy conditional on past observations at the receiver, as a metric of value of information, in contrast to the traditional state-agnostic nonlinear age of information (AoI) penalty functions. To address the limitations of prior UoI research that assumes one-time-slot delays, we extend our analysis to scenarios with random delays. We model the problem as a partially observable Markov decision process (POMDP) problem and simplify it to a semi-Markov decision process (SMDP) by introducing the belief state. We propose two algorithms: A globally optimal bisection relative value iteration (bisec-RVI) algorithm and a computationally efficient sub-optimal index-based threshold algorithm to solve the long-term average UoI minimization problem. Numerical simulations demonstrate that our sampling policies surpass traditional zero wait and AoI-optimal policies, particularly under conditions of large delay, with the sub-optimal policy nearly matching the performance of the optimal one.