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Value of Communication in Goal-Oriented Semantic Communications: A Pareto Analysis

Jiping Luo, Bowen Li, Nikolaos Pappas

TL;DR

This work tackles the value of communication in goal-oriented semantic communications by formulating remote state estimation of Markov sources as a bi-objective MDP. It reveals that the Pareto frontier between estimation cost and communication cost is strictly decreasing, convex, and piecewise linear, with corner points corresponding to stationary deterministic policies and segments realized via convex mixtures. The authors develop SPLIT, an exact, efficient algorithm that constructs the entire frontier by exploiting this structure, with complexity linear in the number of breakpoints. Practically, SPLIT enables hardware-friendly policy selection via a finite lookup of policy pairs and interpolation to adapt to changing budgets, advancing how systems trade off timely, relevant information against transmission constraints. The results connect Lagrangian multipliers to the frontier’s slope, offering precise, implementable value-of-communication metrics for semantics-aware remote estimation and beyond.

Abstract

Emerging cyber-physical systems increasingly operate under stringent communication constraints that preclude the reliable transmission of their extensive machine-type data streams. Since raw measurements often contain correlated or redundant components, effective operation depends not on transmitting all available data but on selecting the information that contributes to achieving the objectives of the system. Beyond accuracy, goal-oriented semantic communication assesses the \emph{value of information} and aims to generate and transmit only what is relevant and at the right time. Motivated by this perspective, this work studies the \emph{value of communication} through the canonical setting of remote estimation of Markov sources, where a value-of-information measure quantifies the relevance of information. We investigate how optimal estimation performance varies with the available communication budget and determine the marginal performance gain attributable to additional communication. Our approach is based on a \emph{Pareto analysis} that characterizes the complete set of policies that achieve optimal trade-offs between estimation performance and communication cost. The value of communication is defined as the absolute slope of the resulting Pareto frontier. Although computing this frontier is non-trivial, we demonstrate that in our setting it admits a notably tractable structure: it is strictly decreasing, convex, and piecewise linear, and its slope is governed by a finite collection of constants. Moreover, each Pareto-optimal operating point is realizable as a convex combination of two stationary deterministic policies, enabling practical implementation. Leveraging these structural insights, we introduce SPLIT, an efficient and provably optimal algorithm for constructing the complete Pareto frontier.

Value of Communication in Goal-Oriented Semantic Communications: A Pareto Analysis

TL;DR

This work tackles the value of communication in goal-oriented semantic communications by formulating remote state estimation of Markov sources as a bi-objective MDP. It reveals that the Pareto frontier between estimation cost and communication cost is strictly decreasing, convex, and piecewise linear, with corner points corresponding to stationary deterministic policies and segments realized via convex mixtures. The authors develop SPLIT, an exact, efficient algorithm that constructs the entire frontier by exploiting this structure, with complexity linear in the number of breakpoints. Practically, SPLIT enables hardware-friendly policy selection via a finite lookup of policy pairs and interpolation to adapt to changing budgets, advancing how systems trade off timely, relevant information against transmission constraints. The results connect Lagrangian multipliers to the frontier’s slope, offering precise, implementable value-of-communication metrics for semantics-aware remote estimation and beyond.

Abstract

Emerging cyber-physical systems increasingly operate under stringent communication constraints that preclude the reliable transmission of their extensive machine-type data streams. Since raw measurements often contain correlated or redundant components, effective operation depends not on transmitting all available data but on selecting the information that contributes to achieving the objectives of the system. Beyond accuracy, goal-oriented semantic communication assesses the \emph{value of information} and aims to generate and transmit only what is relevant and at the right time. Motivated by this perspective, this work studies the \emph{value of communication} through the canonical setting of remote estimation of Markov sources, where a value-of-information measure quantifies the relevance of information. We investigate how optimal estimation performance varies with the available communication budget and determine the marginal performance gain attributable to additional communication. Our approach is based on a \emph{Pareto analysis} that characterizes the complete set of policies that achieve optimal trade-offs between estimation performance and communication cost. The value of communication is defined as the absolute slope of the resulting Pareto frontier. Although computing this frontier is non-trivial, we demonstrate that in our setting it admits a notably tractable structure: it is strictly decreasing, convex, and piecewise linear, and its slope is governed by a finite collection of constants. Moreover, each Pareto-optimal operating point is realizable as a convex combination of two stationary deterministic policies, enabling practical implementation. Leveraging these structural insights, we introduce SPLIT, an efficient and provably optimal algorithm for constructing the complete Pareto frontier.

Paper Structure

This paper contains 19 sections, 16 theorems, 87 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Literature Overview
  3. Goal-Oriented Semantic Communications
  4. Multi-Objective MDPs
  5. System Model
  6. Decision Rules
  7. Performance Criterion
  8. Problem Formulations
  9. Pareto Formulation
  10. Constrained Formulation
  11. Lagrangian Formulation
  12. Pareto Analysis
  13. Monotonicity and Convexity of the Pareto Frontier
  14. Piecewise Linearity of Pareto Frontier
  15. Computing the Pareto Frontier
  16. ...and 4 more sections

Key Result

Lemma 1

A sufficient statistic for the sensor is Therefore, without loss of optimality, it suffices to consider communication policies of the form $U_t \sim \pi_t(\cdot| S_t)$.

Figures (8)

  • Figure 1: Remote state estimation of a Markov source.
  • Figure 2: Time ordering of the relevant variables and decision rules.
  • Figure 3: Illustration of the Pareto frontier (solid line) obtained from (a) the constrained formulation and (b) the Lagrangian formulation. The shaded region represents the set of attainable objective values.
  • Figure 4: Illustration of the cost functions (solid lines) in the Lagrangian formulation and the search for breakpoints.
  • Figure 5: Binary tree representation of Insec for the case in Figure \ref{['fig:search-algorithm']}.
  • ...and 3 more figures

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 1
  • Definition 4
  • Definition 5
  • Theorem 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • ...and 17 more