Loading…
This event has ended. View the official site or create your own event → Check it out
This event has ended. Create your own
View analytic
Monday, December 7 • 19:00 - Saturday, December 12 •18:00
Beyond Convexity: Stochastic Quasi-Convex Optimization

Sign up or log in to save this to your schedule and see who's attending!

This poster has been moved from Monday #86 to Thursday #101.

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD).The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the concept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.


Monday December 7, 2015 19:00 - Saturday December 12, 2015 18:00
210 C #86

Attendees (1)