Optimal Policies for Age and Distortion in a Discrete-Time Model

TL;DR

This paper formulates and solves an optimal policy problem balancing age and distortion costs in a discrete-time setting, using Markov Decision Processes, and extends results to erasure channels and coding scenarios.

Contribution

It introduces a finite-memory policy framework and an efficient algorithm for optimal tradeoff in age-distortion problems, including extensions to erasures and coding.

Findings

Optimal policies can be achieved with finite memory.

The proposed algorithm efficiently finds these policies.

Coding improves performance when payloads are small.

Abstract

We study a discrete-time model where each packet has a cost of not being sent -- this cost might depend on the packet content. We study the tradeoff between the age and the cost where the sender is confined to packet-based strategies. The optimal tradeoff is found by an appropriate formulation of the problem as a Markov Decision Process (MDP). We show that the optimal tradeoff can be attained with finite-memory policies and we devise an efficient policy iteration algorithm to find these optimal policies. We further study a related problem where the transmitted packets are subject to erasures. We show that the optimal policies for our problem are also optimal for this new setup. Allowing coding across packets significantly extends the packet-based strategies. We show that when the packet payloads are small, the performance can be improved by coding.