Communication-efficient and Differentially-private Distributed Nash Equilibrium Seeking with Linear Convergence

TL;DR

This paper proposes a communication-efficient, differentially-private distributed algorithm for Nash equilibrium seeking that guarantees linear convergence and addresses privacy and communication concerns simultaneously.

Contribution

It introduces the CDP-NES framework combining compression and noise addition to ensure privacy and efficiency with proven linear convergence.

Findings

Achieves linear convergence to a neighborhood of the NE.

Guarantees $\

epsilon\

Abstract

The distributed computation of a Nash equilibrium (NE) for non-cooperative games is gaining increased attention recently. Due to the nature of distributed systems, privacy and communication efficiency are two critical concerns. Traditional approaches often address these critical concerns in isolation. This work introduces a unified framework, named CDP-NES, designed to improve communication efficiency in the privacy-preserving NE seeking algorithm for distributed non-cooperative games over directed graphs. Leveraging both general compression operators and the noise adding mechanism, CDP-NES perturbs local states with Laplacian noise and applies difference compression prior to their exchange among neighbors. We prove that CDP-NES not only achieves linear convergence to a neighborhood of the NE in games with restricted monotone mappings but also guarantees $\epsilon$-differential privacy, addressing privacy and communication efficiency simultaneously. Finally, simulations are provided to illustrate the effectiveness of the proposed method.