Nonconvex Optimization

Learning One-hidden-layer ReLU Networks via Gradient Descent
We prove theoretical guarantees of learning one-hidden-layer neural networks with ReLU activations.
Xiao Zhang, Yaodong Yu, Lingxiao Wang, Quanquan Gu
PDF Cite Poster ArXiv Link
Learning One-hidden-layer ReLU Networks via Gradient Descent
A Primal-Dual Analysis of Global Optimality in Nonconvex Low-Rank Matrix Recovery
A primal-dual based framework for analyzing the global optimality of nonconvex low-rank matrix recovery.
Xiao Zhang, Lingxiao Wang, Yaodong Yu, Quanquan Gu
PDF Cite Link
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow
We present a new gradient-based optimization algorithm for inductive matrix completion, which achieves both linear rate of convengence and sample complexities linearly depending on the feature dimension.
Xiao Zhang, Simon Du, Quanquan Gu
PDF Cite Code Poster ArXiv Link
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow
A Unified Framework for Nonconvex Low-rank plus Sparse Matrix Recovery
A unified framework for solving general low-rank plus sparse matrix recovery problems.
Xiao Zhang, Lingxiao Wang, Quanquan Gu
PDF Cite Code Poster ArXiv Link
A Unified Framework for Nonconvex Low-rank plus Sparse Matrix Recovery
A Unified Variance Reduction-Based Framework for Nonconvex Low-Rank Matrix Recovery
A generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery
Lingxiao Wang, Xiao Zhang, Quanquan Gu
PDF Cite Code Poster ArXiv Link
A Unified Computational and Statistical Framework for Nonconvex Low-rank Matrix Estimation
A unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent
Lingxiao Wang, Xiao Zhang, Quanquan Gu
PDF Cite Poster ArXiv Link
Robust Wirtinger Flow for Phase Retrieval with Arbitrary Corruption
A new nonconvex algorithm for robust phase retrieval, which attains a linear rate of convergence and improved statistical error rate.
Jinghui Chen, Lingxiao Wang, Xiao Zhang, Quanquan Gu
PDF Cite ArXiv