Differentially Private Accelerated Distributed Algorithm for Aggregative Optimization.

Area of Science:

• Distributed optimization
• Machine learning
• Data privacy

Background:

• Distributed aggregative optimization (DAO) involves agents whose objectives depend on shared data.
• Frequent information exchange in DAO poses significant privacy risks.
• Existing methods often struggle to balance privacy with algorithmic efficiency.

Purpose of the Study:

• To propose a novel algorithm for DAO that ensures differential privacy.
• To maintain high accuracy and convergence rates despite privacy mechanisms.
• To address the trade-off between data privacy and performance in distributed systems.

Main Methods:

• Developed a differentially private accelerated distributed gradient tracking algorithm.
• Integrated distributed dynamic average consensus, heavy-ball momentum, and differential privacy (DP).
• Employed Laplace noise for privacy and a noise deduction mechanism for accuracy.

Main Results:

• The algorithm achieves linear convergence in mean-square error.
• Explicit suboptimality bounds were derived.
• The algorithm formally satisfies \(\\epsilon \)-differential privacy.

Conclusions:

• The proposed algorithm effectively protects agent privacy in DAO.
• It achieves strong theoretical convergence guarantees and practical accuracy.
• Numerical simulations confirm the method's validity and efficiency.