316. Asymmetric data-driven interdiction problems with cost uncertainty: a distributionally robust optimization approach
Invited abstract in session FB-5: Recent advances in bilevel optimization II, stream Bilevel optimization: strategies for complex decision-making.
Friday, 10:05 - 11:20Room: M:N
Authors (first author is the speaker)
| 1. | Sergei Ketkov
|
| Department of Business Administration, University of Zurich |
Abstract
In this study, we consider a class of bilevel interdiction problems, where the cost coefficients are subject to uncertainty. More precisely, in our problem setting, the cost vector is treated as a random vector, whose probability distribution can only be observed through a finite training data set. Furthermore, both the leader and the follower are assumed to possess limited and potentially asymmetric information about the nominal (true) distribution. In order to address the cost uncertainty, we formulate a bilevel Wasserstein distributionally robust optimization (BDRO) problem, where both decision-makers attempt to hedge themselves against the worst-case distribution and realization of the random cost vector. In the case where the leader has full information about the follower's data set, BDRO with properly defined Wasserstein ambiguity sets and objective criteria is shown to admit a single linear mixed-integer programming (MILP) reformulation. On the other hand, when the leader has only partial or no information about the follower's data, we propose two alternative formulations of BDRO, based, respectively, on oversampling from the leader's data set and a conservative robust approximation. Finally, we explore numerically how the quality of data and decision-maker's risk preferences affect the model's out-of-sample performance.
Keywords
- Data driven optimization
- Optimization under uncertainty and applications
- Multilevel optimization
Status: accepted
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