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Dimension Reduction via Random Projection for Privacy in Multi-Agent Systems

Puspanjali Ghoshal, Ashok Singh Sairam

TL;DR

This work tackles inference privacy in Multi-Agent Systems by introducing a compression-based sanitization that achieves a principled utility-privacy trade-off via robust concepts. The core method, neuronal random projection (NRP), uses per-instance random projection matrices constrained by a Frobenius-norm bound to preserve utility while increasing privacy, and it achieves distance-preserving properties comparable to standard random projection with lower computational cost. The authors formalize utility and privacy as $u_i(T)=\cos(\mathbf{y_i}, T(\mathbf{y_i}))$ and $p_i(T)=1-u_i(T)$, derive $0<||A_i||_F\le \min\{t,2\epsilon_i+\delta\}$ bounds, and establish robustness concepts guiding sanitization. Empirical results on real hospital and synthetic data show NRP outperforms BRP, PCA, and ASUP across breach count, displacement, and resemblance, indicating strong privacy protection with retained utility in MAS settings. The work suggests practical, scalable privacy mechanisms for MAS and points to future work on active adversaries and dynamic agent populations.

Abstract

In a Multi-Agent System (MAS), individual agents observe various aspects of the environment and transmit this information to a central entity responsible for aggregating the data and deducing system parameters. To improve overall efficiency, agents may append certain private parameters to their observations. For example, in a crowd-sourced traffic monitoring system, commuters might share not only their current speed, but also sensitive information such as their location to enable more accurate route prediction. However, sharing such data can allow the central entity or a potential adversary to infer private details about the user, such as their daily routines. To mitigate these privacy risks, the agents sanitize the data before transmission. This sanitization inevitably results in a loss of utility. In this work, we formulate the problem as a utility-privacy trade-off and propose a novel compression-based approach leveraging the notion of robust concepts to sanitize the shared data. We further derive a bound on the norm of the compression matrix required to ensure maximal privacy while satisfying predefined utility constraints.

Dimension Reduction via Random Projection for Privacy in Multi-Agent Systems

TL;DR

This work tackles inference privacy in Multi-Agent Systems by introducing a compression-based sanitization that achieves a principled utility-privacy trade-off via robust concepts. The core method, neuronal random projection (NRP), uses per-instance random projection matrices constrained by a Frobenius-norm bound to preserve utility while increasing privacy, and it achieves distance-preserving properties comparable to standard random projection with lower computational cost. The authors formalize utility and privacy as and , derive bounds, and establish robustness concepts guiding sanitization. Empirical results on real hospital and synthetic data show NRP outperforms BRP, PCA, and ASUP across breach count, displacement, and resemblance, indicating strong privacy protection with retained utility in MAS settings. The work suggests practical, scalable privacy mechanisms for MAS and points to future work on active adversaries and dynamic agent populations.

Abstract

In a Multi-Agent System (MAS), individual agents observe various aspects of the environment and transmit this information to a central entity responsible for aggregating the data and deducing system parameters. To improve overall efficiency, agents may append certain private parameters to their observations. For example, in a crowd-sourced traffic monitoring system, commuters might share not only their current speed, but also sensitive information such as their location to enable more accurate route prediction. However, sharing such data can allow the central entity or a potential adversary to infer private details about the user, such as their daily routines. To mitigate these privacy risks, the agents sanitize the data before transmission. This sanitization inevitably results in a loss of utility. In this work, we formulate the problem as a utility-privacy trade-off and propose a novel compression-based approach leveraging the notion of robust concepts to sanitize the shared data. We further derive a bound on the norm of the compression matrix required to ensure maximal privacy while satisfying predefined utility constraints.

Paper Structure

This paper contains 29 sections, 5 theorems, 37 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Noise-addition based methods
  4. Compression-based methods
  5. Utility-Privacy tradeoff problem
  6. System Model
  7. Quantifying utility and privacy:
  8. Comparative analysis of utility and privacy
  9. Problem Definition
  10. Inference privacy preservation using random projection
  11. Deriving Norm Bounds for the Compression Matrix
  12. Robust Concepts
  13. Compression Methodology: Random Projection
  14. Neuron-friendly or Neuronal random projection
  15. Experiment and results
  16. ...and 14 more sections

Key Result

Theorem 1

Let $\mathcal{P}_{\mathrm{CRLB}} \text{ and } \mathcal{U}_{\mathrm{CRLB}}$ be the privacy and utility values, respectively, computed using the CRLB framework. Similarly, let $\mathcal{P}_{\mathrm{cos}} \text{ and } \mathcal{U}_{\mathrm{cos}}$ denote the corresponding privacy and utility values compu The constants depend on the observation model, sanitization mechanism, and the availability of prio

Figures (5)

  • Figure 1: MAS Architecture
  • Figure 2: Outline of the sanitization process
  • Figure 3: Breach Count Comparison for (a) Real life data (b) Synthetic data
  • Figure 4: Displacement Comparison for (a) Real life data (b) Synthetic data
  • Figure 5: Resemblance Comparison for (a) Real life data (b) Synthetic data

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Definition 3
  • Definition 4
  • Lemma 1
  • Lemma 2
  • ...and 2 more