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Title: Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose the random reshuffling-based gradient-free Optimistic Gradient Descent-Ascent algorithm for solving convex-concave min-max problems with finite sum structure. We prove that the algorithm enjoys the same convergence rate as that of zeroth-order algorithms for convex minimization problems. We deploy the algorithm to solve the distributionally robust strategic classification problem, where gradient information is not readily available, by reformulating the latter into a finite dimensional convex concave min-max problem. Through illustrative simulations, we observe that our proposed approach learns models that are simultaneously robust against adversarial distribution shifts and strategic decisions from the data sources, and outperforms existing methods from the strategic classification literature.  more » « less
Award ID(s):
1743772
NSF-PAR ID:
10356668
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Proceedings of Machine Learning Research
Volume:
151
ISSN:
2640-3498
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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