Timezone: »
In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) no high-order saddle points exists. These results explain why simple algorithms such as stochastic gradient descent have global converge, and efficiently optimize these non-convex objective functions in practice. Our framework connects and simplifies the existing analyses on optimization landscapes for matrix sensing and symmetric matrix completion. The framework naturally leads to new results for asymmetric matrix completion and robust PCA.
Summary/NotesAuthor Information
Rong Ge (Duke University)
Chi Jin (UC Berkeley)
Yi Zheng (Duke University)
Related Events (a corresponding poster, oral, or spotlight)
-
2017 Poster: No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis »
Mon. Aug 7th 08:30 AM -- 12:00 PM Room Gallery
More from the Same Authors
-
2022 Poster: Online Algorithms with Multiple Predictions »
Keerti Anand · Rong Ge · Amit Kumar · Debmalya Panigrahi -
2022 Spotlight: Online Algorithms with Multiple Predictions »
Keerti Anand · Rong Ge · Amit Kumar · Debmalya Panigrahi -
2022 Poster: Extracting Latent State Representations with Linear Dynamics from Rich Observations »
Abraham Frandsen · Rong Ge · Holden Lee -
2022 Spotlight: Extracting Latent State Representations with Linear Dynamics from Rich Observations »
Abraham Frandsen · Rong Ge · Holden Lee -
2021 Poster: Guarantees for Tuning the Step Size using a Learning-to-Learn Approach »
Xiang Wang · Shuai Yuan · Chenwei Wu · Rong Ge -
2021 Spotlight: Guarantees for Tuning the Step Size using a Learning-to-Learn Approach »
Xiang Wang · Shuai Yuan · Chenwei Wu · Rong Ge -
2020 Poster: High-dimensional Robust Mean Estimation via Gradient Descent »
Yu Cheng · Ilias Diakonikolas · Rong Ge · Mahdi Soltanolkotabi -
2020 Poster: Customizing ML Predictions for Online Algorithms »
Keerti Anand · Rong Ge · Debmalya Panigrahi -
2018 Poster: Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator »
Maryam Fazel · Rong Ge · Sham Kakade · Mehran Mesbahi -
2018 Oral: Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator »
Maryam Fazel · Rong Ge · Sham Kakade · Mehran Mesbahi -
2018 Poster: Stronger Generalization Bounds for Deep Nets via a Compression Approach »
Sanjeev Arora · Rong Ge · Behnam Neyshabur · Yi Zhang -
2018 Oral: Stronger Generalization Bounds for Deep Nets via a Compression Approach »
Sanjeev Arora · Rong Ge · Behnam Neyshabur · Yi Zhang -
2017 Poster: How to Escape Saddle Points Efficiently »
Chi Jin · Rong Ge · Praneeth Netrapalli · Sham Kakade · Michael Jordan -
2017 Talk: How to Escape Saddle Points Efficiently »
Chi Jin · Rong Ge · Praneeth Netrapalli · Sham Kakade · Michael Jordan -
2017 Poster: Generalization and Equilibrium in Generative Adversarial Nets (GANs) »
Sanjeev Arora · Rong Ge · Yingyu Liang · Tengyu Ma · Yi Zhang -
2017 Talk: Generalization and Equilibrium in Generative Adversarial Nets (GANs) »
Sanjeev Arora · Rong Ge · Yingyu Liang · Tengyu Ma · Yi Zhang