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A Differentially Private Energy Trading Mechanism Approaching Social Optimum

Yuji Cao, Yue Chen

TL;DR

A privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise is developed, proving that the proposed algorithm achieves $\epsilon $ -differential privacy while converging in expectation to the Nash equilibrium with a suitable step size.

Abstract

This paper proposes a differentially private energy trading mechanism for prosumers in peer-to-peer (P2P) markets, offering provable privacy guarantees while approaching the Nash equilibrium with nearly socially optimal efficiency. We first model the P2P energy trading as a (generalized) Nash game and prove the vulnerability of traditional distributed algorithms to privacy attacks through an adversarial inference model. To address this challenge, we develop a privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise. We prove that the proposed algorithm achieves $ε$-differential privacy while converging in expectation to the Nash equilibrium with a suitable stepsize. Numerical experiments are conducted to evaluate the algorithm's robustness against privacy attacks, convergence behavior, and optimality compared to the non-private solution. Results demonstrate that our mechanism effectively protects prosumers' sensitive information while maintaining near-optimal market outcomes, offering a practical approach for privacy-preserving coordination in P2P markets.

A Differentially Private Energy Trading Mechanism Approaching Social Optimum

TL;DR

A privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise is developed, proving that the proposed algorithm achieves -differential privacy while converging in expectation to the Nash equilibrium with a suitable step size.

Abstract

This paper proposes a differentially private energy trading mechanism for prosumers in peer-to-peer (P2P) markets, offering provable privacy guarantees while approaching the Nash equilibrium with nearly socially optimal efficiency. We first model the P2P energy trading as a (generalized) Nash game and prove the vulnerability of traditional distributed algorithms to privacy attacks through an adversarial inference model. To address this challenge, we develop a privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise. We prove that the proposed algorithm achieves -differential privacy while converging in expectation to the Nash equilibrium with a suitable stepsize. Numerical experiments are conducted to evaluate the algorithm's robustness against privacy attacks, convergence behavior, and optimality compared to the non-private solution. Results demonstrate that our mechanism effectively protects prosumers' sensitive information while maintaining near-optimal market outcomes, offering a practical approach for privacy-preserving coordination in P2P markets.
Paper Structure (19 sections, 5 theorems, 43 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 19 sections, 5 theorems, 43 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Related Work
  4. Contribution and Organization
  5. Peer-to-peer Energy Trading Game
  6. Mathematical Model
  7. Traditional Nash Equilibrium Seeking Algorithm
  8. Adversarial Inference Model
  9. Privacy-preserving Nash Equilibrium Seeking
  10. Algorithm Design
  11. Proof of Properties
  12. Case Studies
  13. Privacy Guarantee
  14. Convergence Analysis
  15. Fidelity Analysis
  16. ...and 4 more sections

Key Result

Proposition 1

In a peer-to-peer energy trading game $\mathcal{G}=\{\mathcal{I}, \mathcal{B}, \Gamma\}$ with a fully connected communication network, suppose the adversary has access to Then, the private coefficient $\beta_i$ (and the corresponding $d_i$) of prosumer $i$ can be accurately inferred by the adversarial inference model eq:infer.

Figures (8)

  • Figure 1: Change of $y_1$ during iterations
  • Figure 2: Distribution of inferred $\hat{d}_1$ of prosumer 1 under different noise levels when attack budget $B = 4$. The red vertical line indicates the true $d_1$ value $15$. The top green progress bar indicates the percentage of data falling within $\pm10$% of the true value.
  • Figure 3: Distribution of inferred $\hat{d}_1$ of prosumer 1 under different attack budgets when noise level $\sigma = 5$. The red vertical line indicates the true ${d}_1$ value $15$. The top green progress bar indicates the percentage of data falling within $\pm10$% of the true value.
  • Figure 4: Heatmap of mean squared inference error.
  • Figure 5: Convergence of Algorithm \ref{['algo-2']} under various perturbations, with the $y$-axis on a logarithmic scale. The solid lines represent the average residual norm, and shaded areas show the variation of the residual norm.
  • ...and 3 more figures

Theorems & Definitions (8)

  • Definition 1: Energy Trading Equilibrium
  • Proposition 1
  • Definition 2: $\mu$-adjacent
  • Definition 3: $\varepsilon$-differential privacy dwork2014algorithmic
  • Theorem 1
  • Theorem 2
  • Lemma 1: Post-Processing dwork2014algorithmic
  • Lemma 2