Distributed Online Convex Optimization With Statistical Privacy

Area of Science:

• Distributed Systems
• Optimization Theory
• Information Security

Background:

• Multiagent systems face challenges in distributed online constrained convex optimization.
• Passive adversaries can compromise agent privacy by corrupting data.
• Existing methods lack robust privacy preservation in such distributed settings.

Purpose of the Study:

• To develop a novel algorithm for distributed online convex optimization that guarantees statistical privacy.
• To address the challenge of a passive adversary corrupting agents and inferring private information.
• To analyze the trade-off between expected regret and statistical privacy.

Main Methods:

• Integration of a correlated perturbation mechanism with globally balanced properties into distributed online (sub)gradient descent.
• Design of the Privacy-Preserving Distributed Online Convex Optimization (PP-DOCO) algorithm.
• Establishment of privacy bounds using Kullback-Leibler divergence (KLD).

Main Results:

• The PP-DOCO algorithm provides statistical privacy guarantees for uncorrupted agents.
• Achieved expected regret of O(sqrt(K)) for convex functions and O(log(K)) for strongly convex functions.
• Demonstrated a trade-off between expected regret and statistical privacy, with performance matching state-of-the-art algorithms.

Conclusions:

• The proposed PP-DOCO algorithm effectively balances statistical privacy and expected regret in distributed online convex optimization.
• The findings offer a significant advancement in securing multiagent systems against passive adversaries.
• Simulation results validate the algorithm's effectiveness and the observed privacy-regret trade-off.