Distributed Adaptive Accelerated Nash Equilibrium Seeking for Noncooperative Games: A Differentially Private Method.

Area of Science:

• Game Theory
• Distributed Algorithms
• Privacy-Preserving Machine Learning

Background:

• Noncooperative games require finding Nash equilibrium.
• Existing algorithms face challenges in privacy and convergence speed.
• Partial-decision information complicates distributed equilibrium seeking.

Purpose of the Study:

• To develop a distributed algorithm for Nash equilibrium seeking.
• To ensure individual privacy protection.
• To achieve fast algorithmic convergence.

Main Methods:

• Utilized a differential privacy mechanism within a consensus-based projected pseudo-gradient algorithm.
• Introduced a novel relaxed inertial method with independent parameter design.
• Designed an adaptive inertia coefficient based on iteration error and a decaying sequence.

Main Results:

• The algorithm quantifies privacy levels and obfuscates shared messages.
• Achieved fast convergence through the relaxed inertial method.
• Demonstrated high flexibility in parameter selection compared to existing methods.

Conclusions:

• The proposed algorithm effectively balances privacy and convergence speed.
• Convergence and differential privacy are analyzed under various stepsize conditions.
• Numerical simulations confirm significant improvements in convergence rate, accuracy, and privacy.