Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization
This work addresses robustness to adversarial and strategic data shifts in machine learning, offering a method for scenarios where gradient information is unavailable, though it is incremental as it builds on existing zeroth-order and min-max optimization techniques.
The authors tackled convex-concave min-max problems, particularly in decision-dependent risk minimization, by proposing a zeroth-order optimistic gradient descent-ascent algorithm with random reshuffling, achieving convergence rates comparable to zeroth-order convex minimization methods and outperforming existing strategic classification approaches in simulations.
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a 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 further specialize the algorithm to solve distributionally robust, decision-dependent learning problems, where gradient information is not readily available. 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.