[论文解读] BRIDGE: Byzantine-resilient Decentralized Gradient Descent

Cheng Fang, Zhixiong Yang+1 more|arXiv (Cornell University)|Aug 21, 2019

Sparse and Compressive Sensing TechniquesEngineering被引用 20

一句话总结

本文提出了BRIDGE，一种拜占庭容错的去中心化梯度下降框架，可在去中心化机器学习系统中任意节点故障的情况下确保收敛。该框架对强凸和非凸问题均实现了可证明的收敛性，收敛速率为O(log t / t)的次线性速率，具备良好的可扩展性，并能有效抵御真实网络中的恶意行为。

ABSTRACT

Machine learning has begun to play a central role in many applications. A multitude of these applications typically also involve datasets that are distributed across multiple computing devices/machines due to either design constraints (e.g., multiagent systems) or computational/privacy reasons (e.g., learning on smartphone data). Such applications often require the learning tasks to be carried out in a decentralized fashion, in which there is no central server that is directly connected to all nodes. In real-world decentralized settings, nodes are prone to undetected failures due to malfunctioning equipment, cyberattacks, etc., which are likely to crash non-robust learning algorithms. The focus of this paper is on robustification of decentralized learning in the presence of nodes that have undergone Byzantine failures. The Byzantine failure model allows faulty nodes to arbitrarily deviate from their intended behaviors, thereby ensuring designs of the most robust of algorithms. But the study of Byzantine resilience within decentralized learning, in contrast to distributed learning, is still in its infancy. In particular, existing Byzantine-resilient decentralized learning methods either do not scale well to large-scale machine learning models, or they lack statistical convergence guarantees that help characterize their generalization errors. In this paper, a scalable, Byzantine-resilient decentralized machine learning framework termed Byzantine-resilient decentralized gradient descent (BRIDGE) is introduced. Algorithmic and statistical convergence guarantees for one variant of BRIDGE are also provided in the paper for both strongly convex problems and a class of nonconvex problems. In addition, large-scale decentralized learning experiments are used to establish that the BRIDGE framework is scalable and it delivers competitive results for Byzantine-resilient convex and nonconvex learning.

研究动机与目标

• 为解决在拜占庭故障存在时缺乏稳健的去中心化学习算法的问题，即节点因被攻破或故障而任意行为的情况。
• 开发一种可扩展的去中心化优化框架，即使部分节点表现出拜占庭行为，也能保持收敛性。
• 在拜占庭条件下，为凸与非凸损失函数提供收敛速率与统计性能的理论保证。
• 弥合拜占庭容错分布式学习与去中心化学习之间的差距，弥补以往工作在可扩展性或收敛性分析方面的不足。

提出的方法

• BRIDGE采用无中心服务器的去中心化梯度下降框架，支持节点间的对等通信。
• 通过利用本地一致性与梯度幅值约束，引入一种鲁棒聚合规则，以过滤恶意更新。
• 算法采用递减步长与自适应权重更新机制，确保在拜占庭节点注入任意梯度的情况下仍能收敛。
• 关键组件是使用李雅普诺夫函数分析稳定性与收敛性，以界定本地模型与最优解之间的偏差。
• 该框架引入一种基于参数化衰减函数的弹性机制，以限制受损梯度的影响。
• 通过考虑拜占庭噪声与随机梯度方差的递归误差界，建立收敛性理论。

实验结果

研究问题

• RQ1 当部分节点表现出拜占庭行为（即任意偏离协议）时，去中心化学习算法是否仍能保持收敛？
• RQ2 拜占庭容错的去中心化优化算法在凸与非凸问题上的收敛速率是多少？
• RQ3 如何在不依赖中心协调器或可信服务器的情况下，实现在去中心化系统中的鲁棒性？
• RQ4 在存在拜占庭故障的情况下，可为泛化误差与样本复杂度提供哪些理论保证？
• RQ5 所提出的框架在对抗性条件下能否扩展至大规模机器学习模型？

主要发现

• BRIDGE对强凸问题及一类非凸问题均实现了O(log t / t)的收敛速率，表明在拜占庭故障下具备次线性但可证明的收敛性。
• 即使多达恒定比例的节点为拜占庭节点，该框架仍能以至少1−δ的概率确保所有非故障节点收敛至最优解。
• 理论分析证实，误差界随时间单调递减，衰减最慢的项为O(log t / t)，该分量决定了整体收敛速率。
• 实验评估表明，BRIDGE在大规模去中心化学习任务中表现出良好的可扩展性，并在凸与非凸设置下均展现出具有竞争力的性能。
• 由于聚合规则中引入了影响受限机制，该算法在拜占庭节点注入大梯度幅值的对抗性梯度时仍保持鲁棒性。
• 实证结果表明，该框架对单节点拜占庭攻击具有弹性，而此类攻击通常会破坏标准的去中心化学习算法。