Managing Distributional Ambiguity in Stochastic Optimization through Statistical Upper Bound Approaches

Regents Of The University Of Michigan - Dearborn, Dearborn MI

Investigators

Abstract

This award will contribute to improving methods for resource allocation decisions when certain features of the problem are highly uncertain and data to estimate uncertain parameters is sparse. Distributionally robust optimization (DRO) is a useful optimization approach when model parameters are uncertain and decision makers are risk averse, but it generally relies on there being enough data available to sufficiently characterize underlying probability distributions. Effectively managing distributional ambiguity is essential for enhancing reliability, efficiency, and sustainability across a wide range of engineering and business domains. This project is motivated by the deployment of electric vehicle (EV) charging infrastructure, where limited data are available for describing geographically distributed demand. To address this issue, the project investigates a statistical bootstrapping approach to develop an upper confidence bound for a population mean - the Average Percentile Upper Bound (APUB). This upper bound serves a dual purpose: it provides not only statistical robustness but also a coherent risk measure, so that decision makers can effectively manage risk of misrepresentation of the underlying distribution. Incorporating APUB into optimization enhances robustness and endows the process with key qualities of data-driven decision-making: reliability, consistency, comprehensibility, and tractability. This award supports the involvement of undergraduate and graduate students in advancing the research agenda. The project is driven by four core objectives, aimed at advancing the field of stochastic optimization and its application to real-world problems like EV charging. These objectives are: (i) Theoretical Foundations: Establish and validate fundamental theorems to confirm the robustness and efficacy of APUB-based data-driven approach. This includes detailed analysis of asymptotic behaviors and the development of methods for optimal parameter tuning to enhance performance. (ii) Computational Advancements: Increase computational efficiency in solving large-scale optimization challenges by creating advanced algorithms specifically designed for multi-stage stochastic issues and improving bootstrap sampling techniques for precise large-scale problem approximations, which enhances scalability. (iii) Framework Flexibility: Improve the adaptability of APUB to various levels of uncertainty, particularly where information is sparse, by applying and optimizing parametric bootstrap methods that can capitalize on limited prior data. (iv) Empirical Validation: The project will rigorously evaluate the effectiveness of the methodology through application in EV charging case studies, providing empirical evidence of their practical value and impact. The project represents a collaboration with the Argonne National Laboratory. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.