Robust and accelerated stochastic approximation approaches for stochastic optimization

Abstract
Recognized as a powerful modeling technique in a diverse set of applications, stochastic optimization remains computationally challenging.  In this talk, we discuss some recent exciting advancement in stochastic approximation (SA) methods applied to stochastic convex optimization.  We first introduce the robust stochastic approximation method and demonstrate that it can substantially outperform the widely used sampling average approximation method (SAA) for certain classes of problems.  We then focus on the stochastic composite optimization, which covers an even wider range of problems.  Although a valid lower bound on the rate of convergence for solving this class of problems was known from the classical complexity theory for convex programming, optimization algorithms that can achieve this lower bound had never been discovered.  We succeeded in solving this problem by proposing an accelerated stochastic approximation method possessing this desired property.  Some promising numerical results will also be presented for solving problems arising from financial risk management and network design under uncertainty.

Biography
Guanghui (George) Lan is currently a Ph.D. candidate in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. He obtained the Master of Science degree in Industrial Engineering from the University of Louisville in 2004. Before that he had spent three years in industry mainly as a software engineer. Guanghui’s research interest lies in stochastic/robust optimization, stochastic approximation, large-scale optimization, and their applications in finance, energy systems, logistics, etc. His academic honors include the INFORMS Computing Society Student Paper Competition Winner and the INFORMS George Nicholson Prize second place in 2008.