Data-Driven Distributionally Robust Stochastic Programming

Ohio State University, The, Columbus OH

Investigators

Abstract

Stochastic programming aids in solving difficult problems with many unknown factors. It does so by relying on probability distributions to mathematically represent and predict uncertain events. However, probabilities of possible outcomes are rarely known in real life. Distributionally robust optimization aims to obtain solutions in the presence of such distributional uncertainties. There are a variety of ways to form distributionally robust stochastic programs. However, which type of model to use for which type of data, system, or decision maker is not well understood. This award supports research to have a deeper understanding of this fundamental question and to explore multi-period uncertainties. The project considers long-term water resources management problems that take various sources of input including climate data, hydrological simulations, expert opinions, and so forth. The results, if successful, will yield improved water management, benefitting the U.S. society and economy. The research findings will be incorporated into educational materials on stochastic optimization. The project will therefore contribute to educating students. The water application will be used to demonstrate the societal impact of our field and to attract women to engineering. To address the problem of effective modeling, the project will attempt a classification of models in a way that highlights how different sources of data and problem characteristics may require differing problem formulations. This research task will use probability theory, statistics, and risk theory to make recommendations. It will then utilize these results to improve modeling and data collection and devise sampling schemes. To address the problem of uncertainty revealed over time, the project will investigate data-driven multistage distributionally robust stochastic programs. This research task will examine how to translate multi-period uncertainties into the model and investigate the resulting model structure and properties. To effectively solve these models, decomposition-based solution methodologies will be explored. In addition, the project will examine the value of data and the effect of different scenarios on optimal solutions and values. Finally, the project will implement the modeling, algorithmic, and theoretical findings to solve real-world multi-period water allocation problems. If successful, the results are also applicable to other problems in energy, transportation, and finance with complex multi-period uncertainties.