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A privacy-preserving distributed credible evidence fusion algorithm for collective decision-making

Chaoxiong Ma, Yan Liang, Xinyu Yang, Han Wu, Huixia Zhang

TL;DR

This work tackles privacy in distributed collective decision-making by proposing PCEF, a privacy-preserving distributed credible evidence fusion algorithm with three-level consensus that mirrors centralized credible fusion (CCEF) when the evidence-difference-measure matrix (EDMM) converges. It leverages privacy-aware EDM neighbor consensus via secure two-party protocols, network-wide EDMM completion through low-rank matrix completion with rank adaptation, and a fusion step using a self-canceling differential privacy term to preserve privacy while achieving consensus akin to CCEF. The approach yields accurate credibility estimates and fusion results close to CCEF, demonstrated through simulations including a 5-category scenario and a UAV swarm radar-signal sorting task, with improvements in decision accuracy and reduced computation time compared to baselines. The framework enables scalable, privacy-conscious distributed inference, with potential extensions to alternative EDMs and blockchain-based protections against malicious fusion attempts.

Abstract

The theory of evidence reasoning has been applied to collective decision-making in recent years. However, existing distributed evidence fusion methods lead to participants' preference leakage and fusion failures as they directly exchange raw evidence and do not assess evidence credibility like centralized credible evidence fusion (CCEF) does. To do so, a privacy-preserving distributed credible evidence fusion method with three-level consensus (PCEF) is proposed in this paper. In evidence difference measure (EDM) neighbor consensus, an evidence-free equivalent expression of EDM among neighbored agents is derived with the shared dot product protocol for pignistic probability and the identical judgment of two events with maximal subjective probabilities, so that evidence privacy is guaranteed due to such irreversible evidence transformation. In EDM network consensus, the non-neighbored EDMs are inferred and neighbored EDMs reach uniformity via interaction between linear average consensus (LAC) and low-rank matrix completion with rank adaptation to guarantee EDM consensus convergence and no solution of inferring raw evidence in numerical iteration style. In fusion network consensus, a privacy-preserving LAC with a self-cancelling differential privacy term is proposed, where each agent adds its randomness to the sharing content and step-by-step cancels such randomness in consensus iterations. Besides, the sufficient condition of the convergence to the CCEF is explored, and it is proven that raw evidence is impossibly inferred in such an iterative consensus. The simulations show that PCEF is close to CCEF both in credibility and fusion results and obtains higher decision accuracy with less time-comsuming than existing methods.

A privacy-preserving distributed credible evidence fusion algorithm for collective decision-making

TL;DR

This work tackles privacy in distributed collective decision-making by proposing PCEF, a privacy-preserving distributed credible evidence fusion algorithm with three-level consensus that mirrors centralized credible fusion (CCEF) when the evidence-difference-measure matrix (EDMM) converges. It leverages privacy-aware EDM neighbor consensus via secure two-party protocols, network-wide EDMM completion through low-rank matrix completion with rank adaptation, and a fusion step using a self-canceling differential privacy term to preserve privacy while achieving consensus akin to CCEF. The approach yields accurate credibility estimates and fusion results close to CCEF, demonstrated through simulations including a 5-category scenario and a UAV swarm radar-signal sorting task, with improvements in decision accuracy and reduced computation time compared to baselines. The framework enables scalable, privacy-conscious distributed inference, with potential extensions to alternative EDMs and blockchain-based protections against malicious fusion attempts.

Abstract

The theory of evidence reasoning has been applied to collective decision-making in recent years. However, existing distributed evidence fusion methods lead to participants' preference leakage and fusion failures as they directly exchange raw evidence and do not assess evidence credibility like centralized credible evidence fusion (CCEF) does. To do so, a privacy-preserving distributed credible evidence fusion method with three-level consensus (PCEF) is proposed in this paper. In evidence difference measure (EDM) neighbor consensus, an evidence-free equivalent expression of EDM among neighbored agents is derived with the shared dot product protocol for pignistic probability and the identical judgment of two events with maximal subjective probabilities, so that evidence privacy is guaranteed due to such irreversible evidence transformation. In EDM network consensus, the non-neighbored EDMs are inferred and neighbored EDMs reach uniformity via interaction between linear average consensus (LAC) and low-rank matrix completion with rank adaptation to guarantee EDM consensus convergence and no solution of inferring raw evidence in numerical iteration style. In fusion network consensus, a privacy-preserving LAC with a self-cancelling differential privacy term is proposed, where each agent adds its randomness to the sharing content and step-by-step cancels such randomness in consensus iterations. Besides, the sufficient condition of the convergence to the CCEF is explored, and it is proven that raw evidence is impossibly inferred in such an iterative consensus. The simulations show that PCEF is close to CCEF both in credibility and fusion results and obtains higher decision accuracy with less time-comsuming than existing methods.

Paper Structure

This paper contains 15 sections, 4 theorems, 37 equations, 11 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. The PCEF algorithm
  4. EDM neighbor consensus
  5. EDM network consensus
  6. EDM collection
  7. Non-neighbored EDMs estimation
  8. Fixed-rank optimization
  9. Rank adjustment
  10. Fusion network consensus
  11. Computational complexity
  12. Simulation
  13. Verification for the approximation of PCEF to CCEF
  14. Comparison experiment
  15. Conclusion

Key Result

Theorem 1

(Evidence fusion consensus) If ${\bf{u}}_i^R \left( {t} \right)$ and ${\bf{u}}_i^{\boldsymbol{\omega}} \left( {t}\right)$ satisfy the following consensus condition: then, the following conslusions hold:

Figures (11)

  • Figure 1: The requirements of DCEF with privacy preservation of raw evidence.
  • Figure 2: Overview of CCEF.
  • Figure 3: The flowchart of PCEF
  • Figure 4: The probability density functions of 5 categories.
  • Figure 5: Simulation results of PCEF
  • ...and 6 more figures

Theorems & Definitions (10)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • Proof 1
  • Theorem 2
  • Proof 2
  • Proposition 1
  • Proposition 2
  • Remark 4