具有交叉耦合混合仿射约束的分散式优化
Decentralized Optimization with Cross-Coupled Mixed Affine Constraints
浏览论文内容
中文总结 AI 辅助
本文研究带交叉耦合混合仿射约束的分散式优化，提出加速方法并给出匹配极小极大保证，实验验证了通道几何与网络条件的影响。
中文摘要 AI 辅助
我们研究具有交叉耦合混合仿射约束的分散式优化问题，其中局部变量和共享变量通过两个仿射通道相互作用。我们表明，将分别良好条件的通道组合起来的内在难度由其弗里德里希斯角决定。这种几何结构产生了一个交叉耦合因子，该因子无法通过逐通道预处理消除，并决定了额外的仿射预言复杂度与通信复杂度。我们开发了一种加速分散式方法，在光滑强凸情形下具有匹配的极小极大保证，并将该框架扩展到光滑和非光滑凸目标。实验证实了所预测的对跨通道几何和网络条件化的依赖关系。
英文摘要
We study decentralized optimization with cross-coupled mixed affine constraints, where local and shared variables interact through two affine channels. We show that the intrinsic difficulty of combining separately well-conditioned channels is governed by their Friedrichs angle. This geometry induces a cross-coupling factor that cannot be removed by channelwise preconditioning and governs the additional affine-oracle and communication complexity. We develop an accelerated decentralized method with matching minimax guarantees in the smooth strongly convex regime and extend the framework to smooth and nonsmooth convex objectives. Experiments confirm the predicted dependence on cross-channel geometry and network conditioning.
