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Goal-Oriented Communications for Remote Inference under Two-Way Delay with Memory

Cagri Ari, Md Kamran Chowdhury Shisher, Elif Uysal, Yin Sun

TL;DR

The paper addresses goal-oriented remote inference over a two-way channel with memory in transmission and feedback delays, where data freshness is captured by the AoI $\Delta(t)$. It formulates a buffered generate-from-buffer model and reduces the problem to minimizing the long-run average inference loss $\mathbb{E}[h(\Delta(t))]$ via a finite-state Markovian delay environment, solved as an average-cost semi-Markov decision process. The main contributions are an explicit index-based threshold scheduling policy with an AoI-channel index $\gamma(\delta,c)$ and a threshold $h_{\psi,opt}$, plus a channel-state dependent buffer mapping $b^* = \psi^*(c)$ that remains optimal under non-monotonic age penalties; in the monotone case the index simplifies and the buffer choice becomes $b^*=0$. Numerical results show substantial gains over IID-delay and generate-at-will baselines, with additional improvements as delay memory increases, underscoring the value of memory-aware, goal-oriented scheduling in next-generation networks.

Abstract

We study the design of a goal-oriented sampling and scheduling strategy through a channel with highly variable two-way random delay, which can exhibit memory (e.g., Delay and Disruption Tolerant Networks). The objective of the communication is to optimize the performance of remote inference, where an inference algorithm (e.g., a trained neural network) on the receiver side predicts a time-varying target signal using the data samples transmitted by a sensor. Previous formulations to this problem either assumed a channel with IID transmission delay, neglecting feedback delay, or considered the monotonic relation that the performance only gets worse as the input information ages. We show how, with delayed feedback, one can effectively exploit the knowledge about delay memory through an index-based threshold policy. This policy minimizes the expected time-average inference error that can be monotone or non-monotone in age. The index function is expressed in terms of the Age of Information (AoI) on the receiver side and a parameter regarding the distribution of subsequent transmission delay, both of which can readily be tracked.

Goal-Oriented Communications for Remote Inference under Two-Way Delay with Memory

TL;DR

The paper addresses goal-oriented remote inference over a two-way channel with memory in transmission and feedback delays, where data freshness is captured by the AoI . It formulates a buffered generate-from-buffer model and reduces the problem to minimizing the long-run average inference loss via a finite-state Markovian delay environment, solved as an average-cost semi-Markov decision process. The main contributions are an explicit index-based threshold scheduling policy with an AoI-channel index and a threshold , plus a channel-state dependent buffer mapping that remains optimal under non-monotonic age penalties; in the monotone case the index simplifies and the buffer choice becomes . Numerical results show substantial gains over IID-delay and generate-at-will baselines, with additional improvements as delay memory increases, underscoring the value of memory-aware, goal-oriented scheduling in next-generation networks.

Abstract

We study the design of a goal-oriented sampling and scheduling strategy through a channel with highly variable two-way random delay, which can exhibit memory (e.g., Delay and Disruption Tolerant Networks). The objective of the communication is to optimize the performance of remote inference, where an inference algorithm (e.g., a trained neural network) on the receiver side predicts a time-varying target signal using the data samples transmitted by a sensor. Previous formulations to this problem either assumed a channel with IID transmission delay, neglecting feedback delay, or considered the monotonic relation that the performance only gets worse as the input information ages. We show how, with delayed feedback, one can effectively exploit the knowledge about delay memory through an index-based threshold policy. This policy minimizes the expected time-average inference error that can be monotone or non-monotone in age. The index function is expressed in terms of the Age of Information (AoI) on the receiver side and a parameter regarding the distribution of subsequent transmission delay, both of which can readily be tracked.
Paper Structure (5 sections, 2 theorems, 35 equations, 3 figures)

This paper contains 5 sections, 2 theorems, 35 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Optimal Scheduling Policy
  4. Simulation Results
  5. Conclusion

Key Result

Theorem 1

If $|h(\delta)|<M$ for all $\delta = 1,2,\ldots$, then the packet submission time sequence $g=(S_{1}(\beta_{\psi}), S_{2}(\beta_{\psi}), ...)$ is an optimal solution to eqn:4, where and $\beta_{\psi}$ is the unique root of where $A_{i}(\beta_{\psi})=S_{i}(\beta_{\psi})+T_i+F_i$ is the $i$-th ACK feedback time and $\Delta(t)=t-S_{i}(\beta_{\psi})+b_i$ is the AoI at time slot $t$. Moreover, $\beta

Figures (3)

  • Figure 1: The remote inference system with two-way communication where the neural network on the receiver side predicts the current value of a target variable using the most recently delivered packet.
  • Figure 2: The incurred inference error when the current sample of the target $Y_{t}$ is predicted using a past sample $X_{t-\delta}$ with AoI $\delta$ ranging from 1 to 70.
  • Figure 3: The time-average inference error achieved by the three different scheduling policies.

Theorems & Definitions (4)

  • Theorem 1
  • proof : Proof sketch
  • Theorem 2
  • proof