Byzantine-Robust Decentralized Stochastic Optimization over Static and Time-Varying Networks

TL;DR

This paper introduces a robust decentralized stochastic optimization method that effectively mitigates Byzantine agent attacks in static and dynamic networks, ensuring convergence near the true solution despite data corruption and malicious behavior.

Contribution

It proposes a TV-norm penalized approach combined with a stochastic subgradient method to handle Byzantine faults in decentralized optimization.

Findings

Method achieves convergence near the Byzantine-free optimal solution.

Robustness demonstrated against Byzantine attacks in numerical experiments.

Outperforms existing methods in robustness and accuracy.

Abstract

In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where the agents collaboratively minimize the summation of expectations of stochastic local cost functions, but some of the agents are unreliable due to data corruptions, equipment failures or cyber-attacks. The unreliable agents, which are called as Byzantine agents thereafter, can send faulty values to their neighbors and bias the optimization process. Our key idea to handle the Byzantine attacks is to formulate a total variation (TV) norm-penalized approximation of the Byzantine-free problem, where the penalty term forces the local models of regular agents to be close, but also allows the existence of outliers from the Byzantine agents. A stochastic subgradient method is applied to solve the penalized problem. We prove that the proposed method reaches a neighborhood of the Byzantine-free optimal solution, and the size of neighborhood is determined by the number of Byzantine agents and the network topology. Numerical experiments corroborate the theoretical analysis, as well as demonstrate the robustness of the proposed method to Byzantine attacks and its superior performance comparing to existing methods.