Suvrajeet Sen
Industrial and Systems Engineering and Electrical Engineering-Systems, University of Southern California
Several emerging applications call for a fusion of statistical learning (SL) and stochastic programming (SP). The Learning Enabled Optimization (LEO) paradigm fuses concepts from these areas in a manner which not only enriches both SL and SP, but also provides a framework which supports rapid model updates and optimization, together with a methodology for model-validation, assessment, and selection. Moreover, in many “big data/big decisions” applications, these steps are repetitive, and realizable only through a continuous cycle of data analysis, optimization, and validation. In order to accommodate such workflow, we adopt a Stochastic Decomposition (SD) framework which is a successive sampling algorithm (also known as incremental sampling) for SP. Under certain assumptions, SD is known to possess the following important properties: a) it produces a solution sequence which converges in expectation, at a rate of approximately O(N^-1) with high probability­; b) it reduces bias and variance simultaneously via a new concept of compromise solutions. For some of the most challenging instances to date, the algorithm has produced near-optimal solutions on desk-top machines within a fraction of the CPU time it takes other methods, such as sample average approximation (SAA) using Benders decomposition and its variants. These properties are particularly important for LEO models which require both SL and SP in the workflow. This lecture will begin with a discussion of LEO models, and their applications. With this motivation, we will review SD, clarifying the methodology and its computations for SP. Finally, we will resume our path to the future where we show how SD provides distribution-free statistical optimality, and supports the LEO workflow, with novel guidelines for model assessment, and selection. Time permitting, we will also present some research challenges for the LEO paradigm. (This work draws upon joint work with several colleagues, as well as current and former students.)