R-DOCO: Resilient Distributed Online Convex Optimization Against Adversarial Attacks

Zhixiang Kong, Huajian Xu and Chengsheng Pan ()
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Zhixiang Kong: School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
Huajian Xu: School of Software, Nanjing University of Information Science and Technology, Nanjing 210044, China
Chengsheng Pan: School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

Mathematics, 2024, vol. 12, issue 21, 1-17

Abstract: This paper addresses the problem of distributed constrained optimization in a multi-agent system where some agents may deviate from the prescribed update rules due to failures or malicious adversarial attacks. The objective is to minimize the collective cost of the unattacked agents while respecting the constraint limitations. To tackle this, we propose a resilient distributed projected gradient descent algorithm for online optimization that achieves sublinear individual regret, defined as the difference between the online and offline solutions. Additionally, we extend the cost function from convex combinations to more general distributed optimization scenarios. The proposed algorithm demonstrates resilience under adversarial conditions, allowing it to handle an unknown number of adversarial nodes while maintaining performance. Compared to existing methods, this approach offers a robust solution to adversarial attacks in constrained distributed optimization problems.

Keywords: distributed projected gradient descent; resilient online optimization; adversarial attack; multi-agent systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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