Privacy-Preserving Distributed ADMM With Event-Triggered Communication.

Area of Science:

• Distributed Systems
• Optimization Theory
• Algorithm Design

Background:

• Distributed optimization involves agents minimizing shared objectives through information exchange.
• Existing methods like ADMM face challenges in privacy and communication efficiency, especially with limited bandwidth.

Purpose of the Study:

• To propose a privacy-preserving and communication-efficient algorithm for distributed optimization problems.
• To address the limitations of existing methods in scenarios with restricted communication.

Main Methods:

• Developed PC-DQM, a decentralized quadratically approximated ADMM algorithm.
• Implemented an event-triggered mechanism to reduce communication frequency.
• Introduced Hessian matrix perturbation for privacy preservation and simplified updates.

Main Results:

• PC-DQM ensures privacy without compromising solution accuracy.
• The algorithm achieves linear convergence to the optimal solution for strongly convex and smooth functions.
• Numerical simulations validate the algorithm's effectiveness and efficiency.

Conclusions:

• PC-DQM offers a robust solution for privacy-preserving distributed optimization under communication constraints.
• The event-triggered approach and Hessian perturbation significantly reduce computational and communication overhead.
• The algorithm demonstrates strong theoretical convergence guarantees and practical performance.