Research
My research lies at the intersection of optimization, statistics, and machine learning. My work focuses on solving fundamental challenges and application problems in data science.
Specifically, I analyze the optimization conditioning of convex and nonconvex problems (such as semidefinite programming and Burer-Monteiro approach for matrix recovery) under statistical assumptions, design statistically and computationally efficient optimization algorithms for data science applications (such as phase retrieval and matrix completion), and study the interplay between model overparametrization, algorithmic regularization, and model generalization in classical and modern machine learning models (such as mixture models and neural networks).
You can check my google scholar for a full list of my work.
Semidefinite programming
Revisiting Spectral Bundle Methods: Primal-dual (Sub)linear Convergence Rates [arxiv] [slides]
Ding and Grimmer
A Strict Complementarity Approach to Error Bound and Sensitivity of Solution of Conic Programs [arxiv]
Ding and Udell
An Optimal-Storage Approach to Semidefinite Programming using Approximate Complementarity [arxiv] [slides]
Ding, Yurtsever, Cevher, Tropp, and Udell
Winner of Student Paper Prize 2019 of INFORMS Optimization Society
On the simplicity and conditioning of low rank semidefinite programs [arxiv]
Ding and Udell
Higher-Order Cone Programming [arxiv] [slides]
Ding and Lim
Working Paper (2018)
Statistical nonconvex optimization
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence [arxiv]
Charisopoulos, Chen, Davis, Diaz, Ding, and Drusvyatskiy
Low-rank matrix recovery with non-quadratic loss: projected gradient method and regularity projection oracle [arxiv]
Ding, Zhang, and Chen
Submitted (2021)
Leave-one-out Approach for Matrix Completion: Primal and Dual Analysis [arxiv] [slides]
Ding and Chen
Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery [arxiv]
Fan, Ding, Chen, and Udell
Overparametrization
Flat minima generalize for low-rank matrix recovery [arxiv] [slides]
Ding, Drusvyatskiy, Fazel, and Harchaoui
Submitted (2022)
Jiang, Chen, and Ding
Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery [arxiv]
Ding, Jiang, Chen, Qu, and Zhu.
Frank-Wolfe
kFW: A Frank-Wolfe style algorithm with stronger subproblem oracles [arxiv] [slides]
Ding, Fan, and Udell
Submitted (2022)
Spectral Frank-Wolfe Algorithm: Strict Complementarity and Linear Convergence [arxiv]
Ding, Fei, Xu, and Yang
Frank-Wolfe Style Algorithms for Large Scale Optimization [arxiv]
Ding and Udell