Submodular Minimax Optimization: Finding Effective Sets
It addresses robust optimization for machine learning applications, offering incremental improvements in specific domains.
The paper tackles the problem of submodular minimax optimization in combinatorial settings, providing a characterization and conditions for finding effective sets, and demonstrates that their algorithms consistently outperform baselines in applications like prompt engineering and ride-sharing.
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) efficient prompt engineering for question answering, (ii) prompt engineering for dialog state tracking, (iii) identifying robust waiting locations for ride-sharing, (iv) ride-share difficulty kernelization, and (v) finding adversarial images. Our experiments demonstrate that our proposed algorithms consistently outperform other baselines.