An Adversary-Resilient Doubly Compressed Diffusion LMS Algorithm for Distributed Estimation

• Published in: Circuits, systems, and signal processing Vol. 41; no. 11; pp. 6182 - 6205
• Main Authors: Zayyani, Hadi, Oruji, Fatemeh, Fijalkow, Inbar
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2022; Springer Nature B.V; Springer Verlag
• Subjects: Algorithms; Circuits and Systems; Computer Science; Cramer-Rao bounds; Criteria; Detectors; Diffusion; Electrical Engineering; Electronics and Microelectronics; Engineering; Instrumentation; Mathematical analysis; Signal,Image and Speech Processing; Statistical tests; Thresholds; Adversary resilient; Distributed estimation; Bayesian hypothesis testing; Communication reduction; Diffusion LMS; Diffusion algorithm; resilience to adverserial attack
• ISSN: 0278-081X; 1531-5878; 1531-5878
• DOI: 10.1007/s00034-022-02072-w

This paper proposes an adversary-resilient communication-efficient distributed estimation algorithm for time-varying networks. It is a generalization of the doubly compressed diffusion least mean square algorithm that is not adversary-resilient. The major drawback in existing adversary detectors in the literature is that they suggested the detection criterion heuristically. In this paper, an adversary detector is suggested theoretically based on a Bayesian hypothesis test (BHT). It is proved that the test statistics of the detectors is a distance metric compared to a threshold similarly to related papers in the literature. Hence, we prove the validity of the detection criterion based on BHT. The other difficulty encountered in existing works is the determination of thresholds. In this paper, the optimum thresholds are derived in closed form. Since the optimum thresholds need the values of unknown parameters, it is not feasible to derive them. Hence, suboptimal procedures for determining the thresholds are provided. Moreover, the convergence of the mean of the algorithm is investigated analytically. In addition, the Cramer–Rao bound of the problem of distributed estimation based on all node observations in the presence of adversaries is calculated. The simulation results show the effectiveness of the proposed algorithms and demonstrate that the proposed algorithms reach the performance of the algorithm when the adversaries are ideally known in advance, with some delay.