Pareto Optimal Algorithmic Recourse in Multi-cost Function

TL;DR

The paper addresses algorithmic recourse under multiple, potentially non-differentiable costs by framing recourse as a multi-objective optimization on an actionability graph and computing Pareto-optimal paths. It introduces a Pareto-shortest-path algorithm based on a modified Bellman-Ford dynamic program that maintains Pareto tables $D^\ell_v$ and prunes dominated paths, with a tunable path-length parameter $\\eta$ for interpretability. To tackle scalability, it adopts an $\\$epsilon$-net based shrinking strategy, yielding a smaller graph $G_\\text{epsilon}$ while preserving approximation guarantees under structured cost functions. Empirical results on MNIST and Adult demonstrate multiple diverse Pareto-optimal recourse paths under different criteria and show the approach scales to larger graphs, validating both theoretical guarantees and practical applicability for transparent, actionable AI decisions.

Abstract

In decision-making systems, algorithmic recourse aims to identify minimal-cost actions to alter an individual features, thereby obtaining a desired outcome. This empowers individuals to understand, question, or alter decisions that negatively affect them. However, due to the variety and sensitivity of system environments and individual personalities, quantifying the cost of a single function is nearly impossible while considering multiple criteria situations. Most current recourse mechanisms use gradient-based methods that assume cost functions are differentiable, often not applicable in real-world scenarios, resulting in sub-optimal solutions that compromise various criteria. These solutions are typically intractable and lack rigorous theoretical foundations, raising concerns regarding interpretability, reliability, and transparency from the explainable AI (XAI) perspective. To address these issues, this work proposes an algorithmic recourse framework that handles non-differentiable and discrete multi-cost functions. By formulating recourse as a multi-objective optimization problem and assigning weights to different criteria based on their importance, our method identifies Pareto optimal recourse recommendations. To demonstrate scalability, we incorporate the concept of epsilon-net, proving the ability to find approximated Pareto optimal actions. Experiments show the trade-off between different criteria and the methods scalability in large graphs. Compared to current heuristic practices, our approach provides a stronger theoretical foundation and better aligns recourse suggestions with real-world requirements.

Figures (4)

• Figure 1: In this example, our approach provides three different paths which are all pareto optimal for the recourse plans. Each path contains different criteria and the user can choose one that fits him the most.
• Figure 2: The paths in MNIST under different criteria of $cost_1$ and $cost_2$.
• Figure 3: Multiple different paths from a starting data point to an end data point. It shows that the algorithm finds multi-criteria paths and can have a diverse path. The four paths show the trade-off between different criteria, which are the KDE, age, education-num, and hours-per-week.
• Figure 4: The trend among different sampling sizes shows that the quality of the Pareto paths becomes better and more stable when the sampling size gets larger. However, the improvement is not that significant when the size is large enough ($\geq 256$).

Theorems & Definitions (4)

• theorem 1
• definition 1
• definition 2
• definition 3