ISyE Seminar Series: Peter Zhang
"Approximating Multiple Robust Optimization Solutions in One Pass via Proximal Point Methods"
Peter Zhang
Assistant Professor, Heinz College of Information Systems and Public Policy
Carnegie Mellon University
About the Seminar:
Robust optimization provides a principled and unified framework to model many problems in modern operations research and computer science applications, such as risk measures minimization and adversarially robust machine learning. To use a robust solution (e.g., to implement an investment portfolio or perform robust machine learning inference), the user has to a priori decide the trade-off between efficiency (nominal performance) and robustness (worst-case performance) of the solution by choosing the uncertainty level hyperparameters. In many applications, this amounts to solving the problem many times and comparing them, each from a different hyperparameter setting. This makes robust optimization practically cumbersome or even intractable. We present a novel procedure based on the proximal point method (PPM) to efficiently approximate many Pareto efficient robust solutions at once. This practically reduces the total compute requirement from $N \times T$ to $2 \times T$, where $N$ is the number of robust solutions to be generated, and $T$ is the time to obtain one robust solution. We prove this procedure can produce exact Pareto efficient robust solutions for a class of robust linear optimization problems. For more general problems, we prove that with high probability, our procedure gives a good approximation of the efficiency-robustness trade-off in random robust linear optimization instances. We conduct numerical experiments to demonstrate.
About the Speaker:
Peter Zhang is an assistant professor at Carnegie Mellon University’s Heinz College of Information Systems and Public Policy. His research focuses on robust optimization, including dynamic and bilevel problems, driven by challenges in transportation safety, workforce resilience, and other topics in policy design and intelligent decision-making in high-stakes environments. His theoretical inquiries are guided by applied projects with industry partners and multi-disciplinary collaborative grants. He obtained PhD from MIT in Engineering Systems, and BASc (Engineering Science) and MASc (Mechanical and Industrial Engineering) from the University of Toronto.
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