Oracle-Driven Stochastic Integer Programming
Abstract
Stochastic Programming is one of the main paradigms for decisions under uncertainty. It supports constrained optimization under conditions where some of the data is uncertain. The main tool used by SP to represent uncertainty is a probability distribution over the set of uncertain events. However, in large multi-faceted organizations like the Navy, uncertainty may be manifest in several forms. In some cases, uncertainty may be modeled via simulations, and inother cases, they may be modeled via a statistical regression representing the best guess, while recognizing error bars which may come from either historical data or errors regarding future trends. Such sources of uncertainty (i.e., simulation or regression) may be represented as oracles which produce a synthetic world which operates while making decisions in a constrainedoptimization setting. This effort is intended to allow models of discrete optimization to interface seamlessly with constrained decision problems. We can also envision that both simulations and regressions providing scenarios at alternative levels of detail within a discrete decision-making context. We will study the mathematical underpinnings of such collections of models, anddesign optimization algorithms which adapt to the level of information that is provided by the oracles. From a mathematical viewpoint, we plan to design new algorithms and study their properties, especially their convergence, bounds on the probability of attaining optimality, and how parallelization can improve the quality of decisions, not simply the speed of decisionmaking.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 17, 2020
- Source ID
- N000142012077
Entities
People
- Suvrajeet Sen
Organizations
- Office of Naval Research
- United States Navy
- University of Southern California