Towards General Certified Robustness of Combinatorial Optimization Solvers

Huaqing Shao, Lanjun Wang, Junchi Yan

Keywords: Certified Robustness; Combinatorial Optimization

TL;DR: We develop a mathematically sound method to certify the robustness of CO solvers and introduce a general robustness enhancement method based on a smoothing concept.

Abstract:

Combinatorial optimization (CO), driven by algorithmic advancements, now spans applications like network design and bioinformatics, crucial for optimizing complex systems and tackling NP-hard problems efficiently across various industries.
Nonetheless, the study for robustness, especially certified robustness in the CO domain which ensures optimization consistency among different data distributions, persists as an unexplored domain.
In this study, we explore the certified robustness and robustness enhancement strategy for CO solvers.
Experiments across datasets and solvers illustrate that our proposed certification definition can achieve a solid robustness guarantee and the enhancement method significantly amplifies the model’s immunity to perturbations in practice.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 9906