Privacy-Preserving Distributed Online Learning With Zeroth-Order Feedback Over Directed Networks

Abstract

This paper investigates a zeroth-order online optimization problem over a directed network, where each node can only access the function value of its local loss after receiving the decision variable, and information exchange among nodes may incur potential privacy leakage risks. To address these challenges, we propose an efficient chaos-encrypted distributed dual averaging algorithm with state decomposition, termed CEDDA-SD. The CEDDA-SD algorithm employs a zeroth-order gradient oracle to effectively overcome the absence of explicit gradient information. Meanwhile, a multi-step accelerated method is incorporated to enhance convergence performance. Furthermore, a combination of state decomposition and chaos encryption strategies is introduced to defend against prevalent privacy inference attacks. Rigorous theoretical analysis establishes that the CEDDA-SD algorithm achieves sublinear expected regret while guaranteeing privacy preservation. Simulations and field-programmable gate array (FPGA) experiments validate the effectiveness of the proposed algorithm and demonstrate its practical advantages in terms of privacy preservation.