Submodular Minimax Optimization: Finding Effective Sets

Loay Mualem, Ethan R. Elenberg, Moran Feldman, Amin Karbasi

Research output: Contribution to journalConference articlepeer-review


Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of submodular minimax optimization, the problem of finding a set (for either the min or the max player) that is effective against every possible response. We show when and under what conditions we can find such sets. We also demonstrate how minimax submodular optimization provides robust solutions for downstream machine learning applications such as (i) prompt engineering in large language models, (ii) identifying robust waiting locations for ride-sharing, (iii) kernelization of the difficulty of instances of the last setting, and (iv) finding adversarial images. Our experiments show that our proposed algorithms consistently outperform other baselines.

Original languageEnglish
Pages (from-to)1081-1089
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2024
Externally publishedYes
Event27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024 - Valencia, Spain
Duration: 2 May 20244 May 2024

Bibliographical note

Publisher Copyright:
Copyright 2024 by the author(s).


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