MoSSP: 基于动量的单环随机惩罚方法用于非凸约束DC正则化优化
MoSSP: A Momentum-Based Single-Loop Stochastic Penalty Method for Nonconvex Constrained DC-Regularized Optimization
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中文总结 AI 辅助
提出MoSSP算法，一种基于动量的单环随机惩罚方法，用于解决具有非凸约束和DC正则化的随机优化问题，实现了O(ε^{-4})和O(ε^{-3})的oracle复杂度。
中文摘要 AI 辅助
本文研究了一类具有差凸（DC）正则化的非凸约束随机问题，其中可行集可能是非凸的，且DC正则化子的凹部分允许非光滑。基本挑战在于在保持非凸约束可行性的同时实现良好的oracle复杂度。尽管单环算法能有效解决无约束DC优化问题，但它们在具有DC结构的约束优化中的潜力尚未被充分探索。为填补这一空白，我们开发了MoSSP，一种基于动量的单环随机惩罚方法，用于此类问题，并具有可证明的复杂度保证。关键思想是将单个随机近端梯度步骤应用于惩罚的Moreau包络加上凸DC部分，同时并行计算凹部分的近端映射。我们推导了两种算法变体：一种具有O(ε^{-4}) oracle复杂度的Polyak动量版本，用于寻找随机ε-KKT点，以及一种改进的O(ε^{-3})版本，结合了递归动量。实验结果证明了所提算法的有效性。
英文摘要
In this paper, we study a structured class of nonconvex constrained stochastic problems with difference-of-convex (DC) regularization, where the feasible set is possibly nonconvex and the concave part of the DC regularizer is allowed to be nonsmooth. The fundamental challenge lies in maintaining feasibility for nonconvex constraints while achieving favorable oracle complexity. Although single-loop algorithms efficiently solve unconstrained DC optimization problems, their potential for constrained optimization with DC structure remains largely unexplored. To address this gap, we develop MoSSP, a Momentum-based Single-loop Stochastic Penalty method for such problems with provable complexity guarantees. The key idea is to apply a single stochastic proximal-gradient step to the Moreau envelope of the penalty plus the convex DC part, with the concave part's proximal mapping computed in parallel. We derive two algorithm variants: a Polyak-momentum version with $O(\varepsilon^{-4})$ oracle complexity for finding stochastic $\varepsilon$-KKT points, and an improved $O(\varepsilon^{-3})$ version incorporating recursive momentum. Experimental results demonstrate the effectiveness of the proposed algorithms.
发表机构
- School of Mathematical Sciences, Beihang University, Beijing 100191, China（北京航空航天大学数学学院）
- School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China（中山大学计算机科学与工程学院）
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