An Approach to Robust Performance Analysis Using Optimal Transport

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The goal of this research is to investigate a comprehensive set of tools to enable robust performance analysis and decision making by building a framework which systematically evaluates the impact of modeling errors. The general philosophy of this research is as follows. Stochastic models are used virtually everywhere and many of these models are convenient because they can be easily calibrated and/or because performance analysis or optimization can be easily done in closed form or algorithmically. But we all recognize that there are trade-offs between the model's fidelity (i.e. their ability to replicate reality) and its tractability. This project investigates a systematic approach which can be used to account for the impact of this trade-off. The PI studies a wide range of models called stochastic networks, which are used to describe virtually any probabilistic system in which there is resource contention. These systems are used in logistics, transportation, communications and systemic risk, among others. The PI plans to apply the developed approach to study robustness questions related to stochastic networks in heavy-traffic utilization and rare events in such systems. This project investigates a comprehensive set of tools which enables the quantification of model errors in the performance analysis and control of a wide range of stochastic systems. The investigator's strategy combines various areas of mathematics, including convex optimization, probability theory, and Monte Carlo methods. The investigator will exploit general duality results which are used to obtain explicit expressions for worst-case expectations among all probability models within a certain tolerance from a baseline probabilistic model (typically chosen for tractability). The metric describing the neighborhood of models is based on optimal transport theory. These results are applicable at the stochastic-process level (for random elements taken values on general Polish spaces), so they can be used to approximate sample-path expectations of complex stochastic systems. A key element in the program is that the worst-case probability of a given event can be expressed explicitly in terms of the probability of a modified (explicit) event under the baseline (tractable) model. The investigator will study a wide range of questions related to rare-event analysis and heavy-traffic approximations of stochastic networks, which are widely used in application areas such as communication networks, call centers, manufacturing systems, and chemical reaction networks, among others.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.