Perfect Counterfactuals in Imperfect Worlds: Modelling Noisy Implementation of Actions in Sequential Algorithmic Recourse

Algorithmic recourse provides actions to individuals who have been adversely affected by automated decision-making and helps them achieve a desired outcome. Knowing the recourse, however, does not guarantee that users would implement it perfectly, either due to environmental variability or personal choices. Recourse generation should thus anticipate its sub-optimal or noisy implementation. While several approaches have constructed recourse that accounts for robustness to small perturbation (i.e., noisy recourse implementation), they assume an entire recourse to be implemented in a single step and thus apply one-off uniform noise to it. Such assumption is unrealistic since recourse often includes multiple sequential steps which becomes harder to implement and subject to more noise. In this work, we consider recourse under plausible noise that adapts to the local data geometry and accumulates at every step of the way. We frame this problem as a Markov Decision Process and demonstrate that the distribution of our plausible noise satisfies the Markov property. We then propose the RObust SEquential (ROSE) recourse generator to output a sequence of steps that will lead to the desired outcome even under imperfect implementation. Given our plausible modelling of sub-optimal human actions and greater recourse robustness to accumulated uncertainty, ROSE can grant users higher chances of success under low recourse costs. Empirical evaluation shows our algorithm manages the inherent trade-off between recourse robustness and costs more effectively while ensuring its low sparsity and fast computation.