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Neuroscheduling for Remote Estimation

Marcos M. Vasconcelos, Yifei Zhang

TL;DR

This work addresses remote estimation where a scheduler reveals only one of two Gaussian sources to a remote estimator, formalizing the objective $\mathbb{E}[ (X_1-\hat X_1)^2+(X_2-\hat X_2)^2 ]$ under a max-scheduling policy. It introduces neuroscheduling, a data-driven approach that uses linear function approximation to model nonlinear estimators via $\eta_j(x)=w_j^T\boldsymbol{\Phi}(x)$ and employs a convex-concave procedure to efficiently train the weights. A key theoretical contribution is a necessary-and-sufficient condition on the basis functions to avoid over-fitting, which explains why simple ReLU-based bases can fail, and numerical results show the optimal scheduler/estimator pair is nonlinear for Gaussian sources. Empirically, soft-plus and polynomial bases yield stable, accurate approximations, suggesting practical pathways to implement adaptive, data-driven scheduling in multi-source remote estimation with performance guarantees against over-fitting.

Abstract

Many modern distributed systems consist of devices that generate more data than what can be transmitted via a communication link in near real time with high-fidelity. We consider the scheduling problem in which a device has access to multiple data sources, but at any moment, only one of them is revealed in real-time to a remote receiver. Even when the sources are Gaussian, and the fidelity criterion is the mean squared error, the globally optimal data selection strategy is not known. We propose a data-driven methodology to search for the elusive optimal solution using linear function approximation approach called neuroscheduling and establish necessary and sufficient conditions for the optimal scheduler to not over fit training data. Additionally, we present several numerical results that show that the globally optimal scheduler and estimator pair to the Gaussian case are nonlinear.

Neuroscheduling for Remote Estimation

TL;DR

This work addresses remote estimation where a scheduler reveals only one of two Gaussian sources to a remote estimator, formalizing the objective under a max-scheduling policy. It introduces neuroscheduling, a data-driven approach that uses linear function approximation to model nonlinear estimators via and employs a convex-concave procedure to efficiently train the weights. A key theoretical contribution is a necessary-and-sufficient condition on the basis functions to avoid over-fitting, which explains why simple ReLU-based bases can fail, and numerical results show the optimal scheduler/estimator pair is nonlinear for Gaussian sources. Empirically, soft-plus and polynomial bases yield stable, accurate approximations, suggesting practical pathways to implement adaptive, data-driven scheduling in multi-source remote estimation with performance guarantees against over-fitting.

Abstract

Many modern distributed systems consist of devices that generate more data than what can be transmitted via a communication link in near real time with high-fidelity. We consider the scheduling problem in which a device has access to multiple data sources, but at any moment, only one of them is revealed in real-time to a remote receiver. Even when the sources are Gaussian, and the fidelity criterion is the mean squared error, the globally optimal data selection strategy is not known. We propose a data-driven methodology to search for the elusive optimal solution using linear function approximation approach called neuroscheduling and establish necessary and sufficient conditions for the optimal scheduler to not over fit training data. Additionally, we present several numerical results that show that the globally optimal scheduler and estimator pair to the Gaussian case are nonlinear.
Paper Structure (10 sections, 3 theorems, 26 equations, 3 figures, 1 table)

This paper contains 10 sections, 3 theorems, 26 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Problem setup
  4. Optimality of Estimator Pairs
  5. Approximation of Nonlinear Estimators
  6. Principles of Linear Function Approximation
  7. Numerical Results
  8. Approximation Using Soft-Plus Functions
  9. Approximation Using Polynomials
  10. Conclusion and Future Work

Key Result

Proposition 1

Suppose the scheduler is desinated to apply the max-scheduling policy as in maxscheduling. Then the corresponding optimal estimators $\eta_1^\star$ and $\eta_2^\star$ are:

Figures (3)

  • Figure 1: Observation-driven sensor scheduling system with two sensors, one scheduler and one receiver.
  • Figure 2: SoftPlus estimator, along with its corresponding scheduling policy, and a validation analysis for a symmetric Gaussian distribution across different correlation values.
  • Figure 3: Polynomial estimator, along with its corresponding scheduling policy, and a validation analysis for a symmetric Gaussian distribution across different correlation values.

Theorems & Definitions (5)

  • Proposition 1
  • Theorem 1
  • proof
  • Corollary 1
  • Remark 1