Distributed Privacy-Preserving Optimization With Accumulated Noise in ADMM

Area of Science:

• Distributed Optimization
• Multiagent Systems
• Privacy Preservation

Background:

• Distributed optimization in multiagent systems faces challenges in preserving individual agent privacy.
• Existing methods may not adequately protect sensitive information during collaborative computations.

Purpose of the Study:

• To propose a novel algorithm, the accumulated noise privacy-preserving alternating direction method of multipliers (ANPPM), for enhanced privacy in distributed optimization.
• To ensure that privacy preservation does not negatively impact the convergence speed or the optimality of the solutions.

Main Methods:

• Agents share masked states with neighbors using a designed noise-adding mechanism.
• An accumulated term is introduced to obfuscate gradients during each iteration.
• The algorithm leverages the alternating direction method of multipliers framework.

Main Results:

• ANPPM ensures privacy preservation for real states and subgradients of each agent.
• The states of all agents are guaranteed to converge to the optimal solution.
• The convergence rate is comparable to the standard ADMM, indicating no adverse effects from the privacy mechanism.

Conclusions:

• The proposed ANPPM algorithm effectively achieves privacy preservation in distributed optimization for multiagent systems.
• ANPPM maintains convergence properties and solution optimality, validated by numerical results.