RED-SEGA：时变网络上基于梯度草图的弹性分散随机近端优化
Resilient Decentralized Stochastic Preconditioned Proximal Optimization with Gradient Sketching over Time-Varying Networks
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中文总结 AI 辅助
研究多智能体系统中拜占庭弹性分散随机优化问题，核心方法是通过梯度草图实现方差减少，提出算法RED-SEGA，推导其在时变网络上的理论条件，经实验验证算法有效性与弹性。
中文摘要 AI 辅助
在多智能体系统的拜占庭弹性分散随机优化中，方差减少对于减轻梯度噪声和增强弹性聚合过程至关重要。然而，现有大多数拜占庭弹性分散方差减少随机梯度算法依赖随机数据采样，在数据稀缺但高维任务中效率低下。本文通过梯度草图实现方差减少。首先构建一类结构风险最小化问题，将梯度草图技术集成到带闲聊通信的分散随机近端梯度下降中，提出分散VR随机梯度算法Gossip-SEGA，又通过用范数惩罚近似代替加权平均开发了其弹性扩展RED-SEGA。理论上推导了RED-SEGA在时变网络上达成共识和线性收敛率的充分条件，数值实验验证了算法的有效性和弹性。
英文摘要
Variance reduction is indispensable in Byzantine-resilient decentralized stochastic optimization over multi-agent systems (MASs), as it effectively mitigates gradient noise to facilitate the resilient aggregation process. However, most existing Byzantine-resilient decentralized variance-reduced (VR) stochastic gradient algorithms rely on random data sampling, which proves inefficient in data-scarce yet high-dimensional tasks, for instance, image deblurring. This paper aims to pursue an alternative approach that achieves variance reduction via gradient sketching. We first formulate a class of structural risk minimization (SRM) problems over time-varying networks, where the local objectives are not necessarily decomposable and their gradients may be inaccessible. To solve the SRM problems in a decentralized manner, we first incorporate a localized gradient-sketching technique into a preconditioned stochastic proximal gradient framework, proposing a novel gossip-based decentralized algorithm with variance reduction, dubbed Gossip-SEGA. To further enhance its resilience, we substitute the weighted-average aggregation in Gossip-SEGA with a norm-penalized approximation, thereby developing a Byzantine-resilient decentralized algorithm, namely RED-SEGA. Theoretically, we derive sufficient conditions for both consensus among reliable agents and (sub)linear convergence rate of RED-SEGA over time-varying networks provided they do not exceed a 50% breakdown point. This is challenging, as the convergence and consensus errors must be bounded within a transformed variable-metric geometry, where the inherent complexities are further compounded by adversarial Byzantine agents and time-varying networks. The effectiveness and resilience of RED-SEGA are validated by solving a constrained least-squares problem and an image deblurring task under various Byzantine attacks.
发表机构
- Hubei Normal University（湖北师范大学）
- City University of Hong Kong（香港城市大学）
- University of New South Wales（新南威尔士大学）
- Southwest University（西南大学）
- Shenzhen University of Advanced Technology（深圳先进技术研究院）
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