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AoI-based Scheduling of Correlated Sources for Timely Inference

Md Kamran Chowdhury Shisher, Vishrant Tripathi, Mung Chiang, Christopher G. Brinton

TL;DR

This work tackles timely inference from multiple correlated remote sources under limited communication by modeling AoI-based scheduling as a non-separable RMAB. It introduces an information-theoretic bound to replace joint penalties with per-source approximations, enabling a tractable gain-index policy (MGF) with performance guarantees for known penalties, and develops online learning (Online-MGF) to handle unknown penalties via bandit feedback. Theoretical results quantify approximation gaps and optimality bounds, while simulations demonstrate scalability and strong performance relative to baselines, even without full model knowledge. The approach offers a practical, scalable framework for timely inference in dense sensor networks and motivates extensions to signal-aware and distributed scheduling.

Abstract

We investigate a real-time remote inference system where multiple correlated sources transmit observations over a communication channel to a receiver. The receiver utilizes these observations to infer multiple time-varying targets. Due to limited communication resources, the delivered observations may not be fresh. To quantify data freshness, we employ the Age of Information (AoI) metric. To minimize the inference error, we aim to design a signal-agnostic scheduling policy that leverages AoI without requiring knowledge of the actual target values or the source observations. This scheduling problem is a restless multi-armed bandit (RMAB) problem with a non-separable penalty function. Unlike traditional RMABs, the correlation among sources introduces a unique challenge: the penalty function of each source depends on the AoI of other correlated sources, preventing the problem from decomposing into multiple independent Markov Decision Processes (MDPs), a key step in applying traditional RMAB solutions. To address this, we propose a novel approach that approximates the penalty function for each source and establishes an analytical bound on the approximation error. We then develop scheduling policies for two scenarios: (i) full knowledge of the penalty functions and (ii) no knowledge of the penalty functions. For the case of known penalty functions, we present an upper bound on the optimality gap that highlights the impact of the correlation parameter and the system size. For the case of unknown penalty functions and signal distributions, we develop an online learning approach that utilizes bandit feedback to learn an online Maximum Gain First policy. Simulation results demonstrate the effectiveness of our proposed policies in minimizing inference error and achieving scalability in the number of sources.

AoI-based Scheduling of Correlated Sources for Timely Inference

TL;DR

This work tackles timely inference from multiple correlated remote sources under limited communication by modeling AoI-based scheduling as a non-separable RMAB. It introduces an information-theoretic bound to replace joint penalties with per-source approximations, enabling a tractable gain-index policy (MGF) with performance guarantees for known penalties, and develops online learning (Online-MGF) to handle unknown penalties via bandit feedback. Theoretical results quantify approximation gaps and optimality bounds, while simulations demonstrate scalability and strong performance relative to baselines, even without full model knowledge. The approach offers a practical, scalable framework for timely inference in dense sensor networks and motivates extensions to signal-aware and distributed scheduling.

Abstract

We investigate a real-time remote inference system where multiple correlated sources transmit observations over a communication channel to a receiver. The receiver utilizes these observations to infer multiple time-varying targets. Due to limited communication resources, the delivered observations may not be fresh. To quantify data freshness, we employ the Age of Information (AoI) metric. To minimize the inference error, we aim to design a signal-agnostic scheduling policy that leverages AoI without requiring knowledge of the actual target values or the source observations. This scheduling problem is a restless multi-armed bandit (RMAB) problem with a non-separable penalty function. Unlike traditional RMABs, the correlation among sources introduces a unique challenge: the penalty function of each source depends on the AoI of other correlated sources, preventing the problem from decomposing into multiple independent Markov Decision Processes (MDPs), a key step in applying traditional RMAB solutions. To address this, we propose a novel approach that approximates the penalty function for each source and establishes an analytical bound on the approximation error. We then develop scheduling policies for two scenarios: (i) full knowledge of the penalty functions and (ii) no knowledge of the penalty functions. For the case of known penalty functions, we present an upper bound on the optimality gap that highlights the impact of the correlation parameter and the system size. For the case of unknown penalty functions and signal distributions, we develop an online learning approach that utilizes bandit feedback to learn an online Maximum Gain First policy. Simulation results demonstrate the effectiveness of our proposed policies in minimizing inference error and achieving scalability in the number of sources.

Paper Structure

This paper contains 23 sections, 8 theorems, 77 equations, 5 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Outline and Summary of Contributions
  3. Related Works
  4. Design of Scheduling Policy
  5. Function Approximation $f_m(\delta_m)$
  6. Scheduling Policy
  7. Lagrangian Relaxation
  8. Gain Index and Threshold Policy
  9. Performance Analysis
  10. Algorithm Simplification
  11. Design of Online Scheduling Policy with Unknown Penalty Function
  12. Online Scheduling for Lagrangian Relaxed Problem
  13. Online Maximum Gain First Policy
  14. Simulation Results
  15. Simulation Model
  16. ...and 8 more sections

Key Result

Lemma 1

If the sequence $(Y_{m, t}, X_{n, t-1}, X_{n, t-k})$ forms a Markov chain $Y_{m, t} \leftrightarrow X_{n, t-1} \leftrightarrow X_{n, t-k}$ for all $k\geq 1$, then the following assertions are true. (a) We have (b) We have where the parameter $\epsilon_{m,n}$ is determined as and $L$-conditional mutual information $I_L( )$ is defined in CMI.

Figures (5)

  • Figure 1: $\beta_k$ vs. Iteration $k$
  • Figure 2: Dis. Sum of Errors vs. $p$ with $M=10$ with $a^2_m=0.9$ in half of sources and other half with $a^2_m=0.7$.
  • Figure 3: Dis. Sum of Errors vs. $p$ with $M=10$ with $a^2_m=0.9$ in all sources.
  • Figure 4: Dis. Sum of Errors vs. $M$ with $p=0.6$
  • Figure 5: Dis. Sum of Errors vs. $M$ with $p=1$

Theorems & Definitions (20)

  • Lemma 1
  • proof
  • Remark 1
  • Theorem 1
  • proof
  • Lemma 2
  • proof
  • Definition 1: Gain Index
  • Theorem 2
  • proof
  • ...and 10 more