IEOR-DRO Seminar: Mengdi Wang (Princeton)

April 11, 2017 | 1:10pm - 2:10pm

IEOR-DRO Seminar: Mengdi Wang (Princeton)

Mudd Hall 303
 
Title: Stochastic Nested Composition Optimization and Beyond
 
Abstract:
Classical stochastic optimization models usually involve expected-value objective functions. However, they do not apply to the minimization of a composition of two or multiple expected-value functions, i.e., the stochastic nested composition optimization problem.
 
Stochastic composition optimization finds wide application in estimation, risk-averse optimization, dimension reduction and reinforcement learning. We propose a class of stochastic compositional first-order methods. We prove that the algorithms converge almost surely to an optimal solution for convex optimization problems (or a stationary point for nonconvex problems), as long as such a solution exists. The convergence involves the interplay of two martingales with different timescales. We obtain rate of convergence results under various assumptions, and show that the algorithms achieve the optimal sample-error complexity in several important special cases. These results provide the best-known rate benchmarks for stochastic composition optimization. 
 
Indeed, stochastic first-order methods provide a basic algorithmic tool for online learning and data analysis. We survey several innovative applications including risk-averse optimization, online principal component analysis, nonconvex statistical optimization, and reinforcement learning.  We will show that rate of convergence analysis of the stochastic optimization algorithms provide sample complexity analysis for these online learning applications.
 
Bio: 
Mengdi Wang’s research focus is stochastic data-driven optimization in machine learning, data analysis, and intelligent systems. She received her PhD from Massachusetts Institute of Technology in 2013 and became an assistant professor at Princeton in 2014. She received the Young Researcher Prize in Continuous Optimization of the Mathematical Optimization Society in 2016 (awarded once every three years), the NSF Career Award in 2017 and the Princeton Engineering Innovation Award in 2017.


500 W. 120th St., Mudd 315, New York, NY 10027    212-854-2942                 
©2014 Columbia University