Privacy-Preserving Distributed Online Optimization Over Unbalanced Digraphs via Subgradient Rescaling

• Published in: IEEE transactions on control of network systems Vol. 7; no. 3; pp. 1366 - 1378
• Main Authors: Xiong, Yongyang, Xu, Jinming, You, Keyou, Liu, Jianxing, Wu, Ligang
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computer simulation; Cost function; Differential privacy; distributed online optimization; expected regret; Graph theory; Heuristic algorithms; Machine learning algorithms; Optimization; Privacy; Rescaling; row-stochasticity; Sensitivity; Trusted third parties; Unbalance; unbalanced digraphs
• ISSN: 2325-5870; 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2020.2976273

In this article, we investigate a distributed online constrained optimization problem with differential privacy where the network is modeled by an unbalanced digraph with a row-stochastic adjacency matrix. To address such a problem, a distributed differentially private algorithm without introducing a trusted third-party is proposed to preserve the privacy of the participating nodes. Under mild conditions, we show that the proposed algorithm attains an <inline-formula><tex-math notation="LaTeX">O(\log T)</tex-math></inline-formula> expected regret bound for strongly convex local cost functions, where <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula> is the time horizon. Moreover, we remove the need for knowing the time horizon <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula> in advance by adopting doubling trick scheme, and derive an <inline-formula><tex-math notation="LaTeX">O(\sqrt{T})</tex-math></inline-formula> expected regret bound for general convex local cost functions. Our results coincide with the best theoretical regrets that can be achieved in the state-of-the-art algorithms. Finally, simulation results are conducted to validate the efficiency of our proposed algorithm.