Tailoring Gradient Methods for Differentially Private Distributed Optimization

• 成果类型: Article
• 署名作者: Wang, Yongqiang; Nedic, Angelia
• 署名单位: Clemson University; Arizona State University; Arizona State University-Tempe
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3272968
• 发表日期: 2024
• 页码: 872-887
• 关键词: Decentralized learning; decentralized optimization; Differential privacy; gradient methods

摘要

Decentralized optimization is gaining increased traction due to its widespread applications in large-scale machine learning and multiagent systems. The same mechanism that enables its success, i.e., information sharing among participating agents, however, also leads to the disclosure of individual agents' private information, which is unacceptable when sensitive data are involved. As differential privacy is becoming a de facto standard for privacy preservation, recently results have emerged integrating differential privacy with distributed optimization. However, directly incorporating differential privacy design in existing distributed optimization approaches significantly compromises optimization accuracy. In this article, we propose to redesign and tailor gradient methods for differentially private distributed optimization, and propose two differential-privacy oriented gradient methods that can ensure both rigorous is an element of-differential privacy and optimality. The first algorithm is based on static-consensus-based gradient methods, and the second algorithm is based on dynamic-consensus (gradient-tracking) based distributed optimization methods and, hence, is applicable to general directed interaction graph topologies. Both algorithms can simultaneously ensure almost sure convergence to an optimal solution and a finite privacy budget, even when the number of iterations goes to infinity. To the best of authors' knowledge, this is the first time that both goals are achieved simultaneously. Numerical simulations using a distributed estimation problem and experimental results on a benchmark dataset confirm the effectiveness of the proposed approaches.