论文标题
春季：非平滑非凸优化的快速随机近端交替方法
SPRING: A fast stochastic proximal alternating method for non-smooth non-convex optimization
论文作者
论文摘要
我们介绍了Spring，这是一种新型随机近端交替线性化最小化算法，用于解决一类非平滑和非凸优化问题。由于数据采集和计算功能的进步，大规模的成像问题越来越普遍。由随机优化方法的成功激发，我们提出了近端交替的线性最小化（PALM）算法的随机变体\ cite {Bolte2014proximal}。我们提供全局收敛的保证，表明我们提出的具有差异的随机梯度估计器的方法，例如saga \ cite {saga}和sarah \ cite {sarah}，可以实现最先进的甲骨文甲骨文复杂性。我们还通过几个数值示例，包括稀疏的非阴性基质分解，稀疏主成分分析和盲图像反卷积，证明了算法的功效。
We introduce SPRING, a novel stochastic proximal alternating linearized minimization algorithm for solving a class of non-smooth and non-convex optimization problems. Large-scale imaging problems are becoming increasingly prevalent due to advances in data acquisition and computational capabilities. Motivated by the success of stochastic optimization methods, we propose a stochastic variant of proximal alternating linearized minimization (PALM) algorithm \cite{bolte2014proximal}. We provide global convergence guarantees, demonstrating that our proposed method with variance-reduced stochastic gradient estimators, such as SAGA \cite{SAGA} and SARAH \cite{sarah}, achieves state-of-the-art oracle complexities. We also demonstrate the efficacy of our algorithm via several numerical examples including sparse non-negative matrix factorization, sparse principal component analysis, and blind image deconvolution.
