Henry Lam, from the Industrial Engineering and Operations Research Department at Columbia University, will present a talk at the Applied Mathematics Colloquium.


Title: Enhancing efficiency and flexibility of stochastic gradient estimation

Abstract:
Stochastic gradient estimation arises in the optimization and uncertainty quantification of models where the function outputs or gradients can only be noisily evaluated. In this talk, I will present two recent works on this methodology. First is the development of an approach to compute the gradients of artificial neural networks in substitute of the widely used backpropagation algorithm, based on the so-called push-out likelihood ratio method. This approach aims to remove the differentiability requirements and consequently expand the choices of the loss and the activation functions in training. Second is an enhancement of the conventional finite-difference method that achieves a universally better estimation accuracy, by using a weighting scheme judiciously constructed based on a minimax analysis to balance bias and variance. The talk is based on joint work with Michael Fu, Bernd Heidergott, Jeff Hong, Yijie Peng, Li Xiao, Xinyu Zhang and Xuhui Zhang.

Biography:
Prof. Lam researches Monte Carlo simulation and optimization under uncertainty. His work focuses on the quantification and mitigation of statistical errors and risks in integrating these methodologies with data, and the design and analysis of efficient computation and solution machineries. Henry is also broadly interested in the intersecting domains of computational probability, stochastic and robust optimization, and machine learning.

He builds methods for computational simulation and optimization used in data-driven decision-making. The complexities in modern industrial and business applications make it challenging to devise these methods using conventional statistical tools, due to the high-dimensionality of uncertain input or model space, heavy computation burden in high-fidelity simulation models, and structural complexities in data utilization in decision-making. Lam develops techniques that are both statistically and computationally efficient to address these challenges. These techniques are used, for example, to assess the propagation and aggregation of uncertainties from input and model calibration in large-scale stochastic simulation, to validate and enhance the performances of solutions in uncertain optimization, and to manage risks stemming from extreme events. His application areas include autonomous vehicle testing, financial risk analytics and online marketing.

Prof. Lam received his PhD degree in statistics from Harvard University in 2011 and was on the faculty of Boston University and the University of Michigan before joining Columbia in 2017. He is a recipient of the NSF CAREER Award in 2017 and serves on the editorial boards of Operations Research and INFORMS Journal on Computing.