论文标题
在静态和时变网络上，拜占庭式分散的随机优化
Byzantine-Robust Decentralized Stochastic Optimization over Static and Time-Varying Networks
论文作者
论文摘要
在本文中，我们考虑了在分散的静态和时间变化网络上定义的拜占庭式随机优化问题，在该网络中，代理商协作可最大程度地减少随机本地成本功能的期望的总和，但是由于数据损坏，设备故障或网络攻击，某些代理商是不可靠的。此后称为拜占庭式药物的不可靠药物可以向其邻居发送错误的值并偏向优化过程。我们处理拜占庭式攻击的主要思想是制定无拜占庭问题问题的总变化（TV）规范式的近似，在这种情况下，罚款项会迫使常规代理的当地模型接近，但也允许从拜占庭代理人那里存在异常值。使用随机亚级别方法来解决刑罚问题。我们证明所提出的方法到达无拜占庭最佳解决方案的邻域，邻居的大小由拜占庭式药物的数量和网络拓扑确定。数值实验证实了理论分析，并证明了拜占庭攻击的拟议方法的鲁棒性及其与现有方法相比的出色性能。
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.
