Statistics and Data Science Seminar
Rishi Sonthalia
UCLA
Project and Forget: Solving Highly Constrained Optimization Problems
Abstract: Many important machine learning problems can be formulated as highly constrained convex optimization problems. One important example is metric constrained problems. In this paper, we show that standard optimization techniques can not be used to solve metric constrained problem.
To solve such problems, we provide a general active set framework, called Project and Forget, and several variants thereof that use Bregman projections. Project and Forget is a general purpose method that can be used to solve highly constrained convex problems with many (possibly exponentially) constraints. We provide a theoretical analysis of Project and Forge} and prove that our algorithms converge to the global optimal solution and have a linear rate of convergence.
In this talk I will go over the main details of the algorithm, the convergence results and applications to metric constrained and non metric constrained problems. For the non metric constrained problem I will present an application to a new formulation of unbalanced optimal transport known as dual regularized optimal transport.
Wednesday March 9, 2022 at 4:00 PM in Zoom