ABSTRACT: The past few years have witnessed growing interest in the development of easily implementable parameter-free first-order methods to facilitate their applications, e.g., in data science and machine learning. In this talk, I will discuss some recent progresses that we made on uniformly optimal methods for convex and nonconvex optimization. By uniform optimality, we mean that these algorithms do not require the input of any problem parameters but can still achieve the best possible iteration complexity bounds for solving different classes of optimization problems. We first consider convex optimization problems under different smoothness levels and show that neither such smoothness information nor line search procedures are needed to achieve uniform optimality. We then consider regularity conditions (e.g., strong convexity and lower curvature) that are imposed over a global scope and thus are notoriously more difficult to estimate. By presenting novel methods that can achieve tight complexity bounds to compute solutions with verifiably small (projected) gradients, we show that such regularity information is in fact superfluous for handling strongly convex and nonconvex problems. It is worth noting that our complexity bound for nonconvex problems also appears to be new in the literature.

BIO: Guanghui (George) Lan is an A. Russell Chandler III Chair and professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Lan was on the faculty of the Department of Industrial and Systems Engineering at the University of Florida from 2009 to 2015, after earning his Ph.D. degree from Georgia Institute of Technology in August 2009. His main research interests lie in optimization, machine learning, and reinforcement learning along with their applications in sustainability and healthcare. The academic honors he received include the INFORMS Frederick W. Lanchester Prize (2023), the INFORMS Computing Society Prize (2022), the National Science Foundation CAREER Award (2013), INFORMS Junior Faculty Interest Group Paper Competition First Place (2012), and the Mathematical Optimization Society Tucker Prize Finalist (2012). Dr. Lan serves as an associate editor for Mathematical Programming, SIAM Journal on Optimization, Operations Research, and Computational Optimization and Applications. He is also an associate director of the Center for Machine Learning at Georgia Tech.