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1589. Computationally Efficient Data-Driven Distributional Robustness Over Time

Invited abstract in session TD-34: Trends and Open Problems in Robust Optimization, stream Stochastic, Robust and Distributionally Robust Optimization.

Tuesday, 14:30-16:00
Room: 43 (building: 303A)

Authors (first author is the speaker)

1. Frauke Liers
Department Mathematik, FAU Erlangen-Nuremberg
2. Kevin-Martin Aigner
Friedrich-Alexander-Universität Erlangen-Nürnberg
3. Andreas Bärmann
FAU Erlangen-Nürnberg
4. Kristin Braun
Friedrich-Alexander-Universität Erlangen-Nürnberg
5. Sebastian Pokutta
Zuse Institute Berlin
6. Kartikey Sharma
AISST, Zuse Institute Berlin

Abstract

Stochastic Optimization (SO) typically requires knowledge about the
probability distribution of uncertain parameters. As the latter is
often unknown, Distributionally Robust Optimization (DRO) provides a
strong alternative that determines the best guaranteed solution over a
set of distributions (ambiguity set). We present an approach for DRO
over time that uses online learning and scenario observations arriving
as a data stream to learn more about the uncertainty. Our robust
solutions adapt over time and reduce the cost of protection with
shrinking ambiguity. For various kinds of ambiguity sets, the robust
solutions converge to the SO solution. Our algorithm achieves the
optimization and learning goals without solving the DRO problem
exactly at any step. We also provide a regret bound for the quality of
the online strategy and also discuss how to perform a scenario
reduction with approximation guarantee. We illustrate the
effectiveness of our procedure by numerical experiments from popular benchmark libraries and give practical examples stemming from telecommunications and routing. Our algorithm is able to solve the DRO over time problem significantly faster than standard reformulations.

This talk is based on joint work with K. Aigner, A. Bärmann, K. Braun,
S. Pokutta, O. Schneider, K. Sharma, S. Tschuppik. Parts of the talk
are published in INFORMS J Optimization, 2023.

Keywords

Status: accepted

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