Robust Bayesian recourse.

Algorithmic recourse aims to recommend an informative feedback to overturn an unfavorable machine learning decision. We introduce in this paper the Bayesian recourse, a model-agnostic recourse that minimizes the posterior probability odds ratio. Further, we present its min-max robust counterpart with the goal of hedging against future changes in the machine learning model parameters. The robust counterpart explicitly takes into account possible perturbations of the data in a Gaussian mixture ambiguity set prescribed using the optimal transport (Wasserstein) distance. We show that the resulting worst-case objective function can be decomposed into solving a series of two-dimensional optimization subproblems, and the min-max recourse finding problem is thus amenable to a gradient descent algorithm. Contrary to existing methods for generating robust recourses, the robust Bayesian recourse does not require a linear approximation step. The numerical experiment demonstrates the effectiveness of our proposed robust Bayesian recourse facing model shifts. Our code is available at https://github.com/VinAIResearch/robust-bayesian-recourse.