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

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

TL;DR

The paper tackles real-time remote inference where a receiver predicts $Y_t$ from remote samples using a pre-trained model, with scheduling decisions on when to send and how many samples per packet under two-way Markovian delays. It casts the problem as an infinite-horizon average-cost SMDP and derives two optimal policies: a closed-form, time-invariant packet-length policy with an index-based waiting-time rule and a buffer-position selection, and a generalized policy allowing time-variable packet lengths with a reduced-complexity solution. Central to both is an index function $\gamma(\cdot)$ and a unique optimal value $\varepsilon_{\cdot,\text{opt}}$ that serve as thresholds for decisions, capturing the non-monotonic relationship between AoI and inference accuracy. Simulations on AR processes and a cart-pole task demonstrate dramatic gains over AoI-first strategies, including up to a six-fold reduction in inference error and substantial gains from adapting packet length to delay memory.

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.

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

TL;DR

The paper tackles real-time remote inference where a receiver predicts from remote samples using a pre-trained model, with scheduling decisions on when to send and how many samples per packet under two-way Markovian delays. It casts the problem as an infinite-horizon average-cost SMDP and derives two optimal policies: a closed-form, time-invariant packet-length policy with an index-based waiting-time rule and a buffer-position selection, and a generalized policy allowing time-variable packet lengths with a reduced-complexity solution. Central to both is an index function and a unique optimal value that serve as thresholds for decisions, capturing the non-monotonic relationship between AoI and inference accuracy. Simulations on AR processes and a cart-pole task demonstrate dramatic gains over AoI-first strategies, including up to a six-fold reduction in inference error and substantial gains from adapting packet length to delay memory.

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.

Paper Structure

This paper contains 18 sections, 2 theorems, 51 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. Communication Network Model
  5. Inference Error as a Function of AoI and Packet Length
  6. Structure of the Scheduling Policy
  7. Learning and Communications Co-design: Time-invariant Packet Length Selection
  8. Co-design Problem Formulation
  9. Optimal Solution to \ref{['Problem 1: Inner opt problem']}-\ref{['Problem 1: Outer opt problem']}
  10. Learning and Communications Co-design: Time-Variable Packet Length Selection
  11. Co-design Problem Formulation
  12. Optimal Solution to \ref{['Problem 3']}
  13. Simulations
  14. Model-Based Evaluation
  15. Trace-Driven Evaluation
  16. ...and 3 more sections

Key Result

Theorem 1

There exists an optimal solution $\pi^* = ((b_2^*, b_3^*, \ldots), (l, l, \ldots), (\tau_2^*, \tau_3^*, \ldots)) \in \Pi_l$ to problem Problem 1: Inner opt problem, where the optimal waiting time $\tau_{i+1}^*$ is determined by the index-based threshold rule the optimal buffer position $b_{i+1}^*$ is given by $\mathfrak{D} = F_{i+1}+\tau_l(b+T_{i+1}(l)+F_{i+1}, C_{i+1})+T_{i+2}(l)$, and $\gamma(

Figures (9)

  • Figure 1: A remote inference system that adopts the selection-from-buffer medium access model shisher2024timelyshisher2022does.
  • Figure 2: An illustration of the $i$-th and the $(i+1)$-th packet transmission epochs.
  • Figure 3: Inference error of the AR process for AoI values ${\delta = 1, 2, \ldots, 50}$ and packet lengths $l=1, 2, 4, 6, 8, 10$.
  • Figure 4: Time-average inference error vs. the scaling parameter $\sigma$ of transmission delay $T_i(l)$.
  • Figure 5: Time-average inference error vs. the sum of transition probabilities $\alpha = p_{12} + p_{21}$.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof : Proof Sketch
  • Theorem 2
  • proof : Proof Sketch