The objective of this Faculty Early Career Development (CAREER) award is to develop foundational theory and efficient computational tools for an important class of data-driven stochastic optimization problems, stochastic nested composition optimization. These nested composition problems arise in many areas such as risk management, machine learning, and online decision making, and are not amenable to classical methods of stochastic optimization. On the theory and methodology side, the project will advance both optimization and data analytics. On the education side, the project will result in curricular innovation that integrates optimization and data analytics in a unified way and offers new case studies on practical applications. The project will promote underrepresented minority students by involving them in frontier research. The research will produce new algorithms and analysis tools that will be useful for many data-intensive applications. These methods will be empirically tested in a collaborative project with a local healthcare system, with the goal of improving healthcare delivery by reducing cost and improving quality of service.
Stochastic nested composition optimization constitutes a new class of stochastic optimization problems that involve nested nonlinear composition of multiple expectations and multi-level random variables. This project will (a) establish the basic complexity theory for two-level and multi-level stochastic nested composition optimization and their generalizations; (b) develop efficient algorithms that process streaming data with theoretical guarantees; (c) investigate several special cases of the problem and apply the results to modeling and optimizing healthcare decisions based on real clinical data (obtained through the collaboration with a NJ-based hospital chain); and (d) develop innovative curricula and research projects that can bring students at various levels to frontier technology. The nested composition provides a rich modeling tool for applications that require data-driven decision-making and optimization under uncertainty. A critical challenge is that the objective is no longer a linear functional of the data distribution, and thus existing theory and methods are inappropriate. The nonlinearity with respect to the distribution of data makes the problem fundamentally more difficult than most of the classical problems. Overcoming the analytical challenge calls for an integration of mathematical programming and stochastic analysis. If successful, the research will make a substantial contribution by expanding the scope of stochastic optimization. Theoretically, it will strengthen our mathematical understanding of stochastic optimization and establish foundational sample complexity bounds. Methodologically, it will provide new algorithms and analysis tools for several important problems in data-driven optimization and online learning. The results will establish important connections among several areas in mathematical programming, statistics, and machine learning.
