Goal-Oriented Status Updating for Real-time Remote Inference over Networks with Two-Way Delay (2410.08706v3)

Abstract: We study a setting where an intelligent model (e.g., a pre-trained neural network) predicts the real-time value of a target signal using data samples transmitted from a remote source according to a scheduling policy. The scheduler decides on i) the age of the samples to be sent, ii) when to send them, and iii) the length of each packet (i.e., the number of samples contained in each packet). The dependence of inference quality on the Age of Information (AoI) for a given packet length is modeled by a general relationship. Previous work 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 (ii) for any constant packet length. The solution for when to send is an index-based threshold policy, where the index function is expressed in terms of the delay state and AoI at the receiver. The age of the packet selected is a function of the delay state. We separately optimize the value of the constant length. We also develop an index-based threshold policy for the variable 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 age-based scheduling of unit-length packets.