报告题目：Accelerating Sparse Over-parameterized Solvers via Fast Inexact Gradients

报告时间：2025年4月18日（周五）下午14:00-16:00

报告地点：南一120

主讲人：梁经纬 副教授

摘要：Sparse regularization, such as $\ell_1$-norm, (over-lapping) group sparsity and low-rank, are widely used in data science and machine learning. Designing efficient numerical solvers for sparse regularization has been an extremely active research area since the new millennium. Recently, over-parameterized solvers such as VarPro [Poon & Peyre, 2023] have been particularly attractive due to its improved conditioning properties and ability to transform the original non-smooth optimization problem into a smooth one, enabling the possibilities of adopting high-order numerical schemes such as quasi-Newton methods. However, despite the fast global convergence behavior, such methods incur a high per iteration complexity. To circumvent this drawback, by an “approximated dimension reduction'”, in this talk I will introduce an inexact version of VarPro which can significantly reduce the per-iteration complexity. The error incurred at each step can be directly controlled and our inexact gradient approach is adaptive, thus allowing for significant acceleration without hurting convergence. The method works seamlessly with L-BFGS and substantially enhances the performance of VarPro. Numerical experiments are provided for various sparse optimization problems.

梁经纬，副教授，上海交通大学自然科学研究院。梁经纬于2013年获得上海交通大学数学硕士学位，之后于2016年获得法国卡昂大学数学博士学位。2017至2020年，梁经纬在英国剑桥大学理论物理与应用数学系从事博士后研究工作，并于2020年底加入伦敦玛丽王后大学数学科学学院任数据科学讲师。2021年7月，加入上海交通大学。梁经纬的主要研究兴趣为数学图像处理，非光滑优化和数据科学等。