Goal-Oriented Status Updating for Real-time Remote Inference over Networks with Two-Way Delay

TL;DR

This paper develops a goal-oriented scheduling framework for real-time remote inference that optimizes packet transmission policies considering non-monotone age dependence and Markovian delays, significantly reducing inference error.

Contribution

It introduces a novel semi-Markov decision process model and derives index-based threshold policies for optimizing transmission timing and packet length in remote inference systems.

Findings

Achieves a sixfold reduction in inference error compared to age-based scheduling.

Provides a closed-form solution for transmission and freshness decisions under complex delay models.

Develops an index-based policy for variable packet lengths that reduces computational complexity.

Abstract

We study a setting where an intelligent model (e.g., a pre-trained neural network) infers the real-time value of a target signal using data samples transmitted from a remote source. The transmission scheduler decides (i) the freshness of packets, (ii) their length (i.e., the number of samples they contain), and (iii) when they should be transmitted. The freshness is quantified using the Age of Information (AoI), and the inference quality for a given packet length is a general function of AoI. Previous works assumed i.i.d. transmission delays with immediate feedback or were restricted to the case where inference performance degrades as the input data ages. Our formulation, in addition to capturing non-monotone age dependence, also covers Markovian delay on both forward and feedback links. We model this as an infinite-horizon average-cost Semi-Markov Decision Process. We obtain a closed-form solution that decides on (i) and (iii) for any constant packet length. The solution for when to transmit is an index-based threshold policy, where the index function is expressed in terms of the delay state and AoI at the receiver. In contrast, the freshness of the selected packet is a function of only the delay state. We then separately optimize the value of the constant packet length. Moreover, we also develop an index-based threshold policy for the time-variable packet length case, which allows a complexity reduction. In simulation results, we observe that our goal-oriented scheduler drops inference error down to one-sixth with respect to the age-based scheduling of unit-length packets.