Teacher:In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Teacher: Now, understand the problem? Solve this instance: We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms for minimizing such functions. Our results imply that these efficient algorithms are statistically stable and also generalize well. In particular, we derive fast rates which resemble the bounds that are often attained in the strongly convex setting. We specify our bounds to Principal Component Analysis and Independent Component Analysis. Our results and techniquesmay pave the way for statistical analyses of additional strict saddle problems.
Student:
Fast Rates for Empirical Risk Minimization of Strict Saddle Problems