A Zeroth-order Resilient Algorithm for Distributed Online Optimization against Byzantine Edge Attacks
Yuhang Liu, Wenjun Mei
TL;DR
This work addresses distributed online convex optimization in networks subject to time-varying Byzantine edge attacks, where agents only observe point evaluations of their local objectives. It introduces a zeroth-order algorithm based on deterministic finite-difference gradient estimates and a Byzantine-resilient consensus mechanism that operates over a filtered neighbor set with a row-stochastic weight construction. The authors prove consensus among agents and derive dynamic-regret bounds that are sublinear in time under appropriate step-size choices, supported by simulations. The approach extends gradient-free distributed optimization to adversarial, time-varying environments, offering a practical tool for secure multi-agent learning and optimization.
Abstract
In this paper, we propose a zeroth-order resilient distributed online algorithm for networks under Byzantine edge attacks. We assume that both the edges attacked by Byzantine adversaries and the objective function are time-varying. Moreover, we focus on the scenario where the complete time-varying objective function cannot be observed, and only its value at a certain point is available. Using deterministic difference, we design a zeroth-order distributed online optimization algorithm against Byzantine edge attacks and provide an upper bound on the dynamic regret of the algorithm. Finally, a simulation example is given justifying the theoretical results.