提出新型随机算法求解分层变分不等式问题，兼顾效率与理论保障。
Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities
- 设计带方差缩减的随机外梯度方法，处理双层结构优化问题。
- 首次在欧氏与Bregman框架下给出收敛速率和复杂度证明。
- 适用于机器学习中的分层优化场景，如元学习与对抗训练。
我们从变分不等式（VIs）的角度研究广义优化问题——这类问题极为通用，涵盖函数最小化、鞍点（极小极大）问题、纳什均衡等众多情形。本研究的核心挑战在于问题的双层分层结构，以及每层平滑算子的有限求和表示。针对该设定，本文首次在欧氏与Bregman框架下，为基于方差缩减的随机算法提供了收敛速率与复杂度分析，证明了其逼近分层变分不等式解的有效性。
原文摘要 · Abstract (English)
We are concerned with optimization in a broad sense through the lens of solving variational inequalities (VIs) -- a class of problems that are so general that they cover as particular cases minimization of functions, saddle-point (minimax) problems, Nash equilibrium problems, and many others. The key challenges in our problem formulation are the two-level hierarchical structure and finite-sum representation of the smooth operators in each level. For this setting, we are the first to prove convergence rates and complexity statements for variance-reduced stochastic algorithms approaching the solution of hierarchical VIs in Euclidean and Bregman setups.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。