Machine learning models now influence decisions that directly affect people's lives, making it important to understand not only their predictions, but also how individuals could act to obtain better results. Algorithmic recourse provides actionable input modifications to achieve more favorable outcomes, typically relying on counterfactual explanations to suggest such changes. However, when the Rashomon set - the set of near-optimal models - is large, standard counterfactual explanations can become unreliable, as a recourse action valid for one model may fail under another. We introduce ElliCE, a novel framework for robust algorithmic recourse that optimizes counterfactuals over an ellipsoidal approximation of the Rashomon set. The resulting explanations are provably valid over this ellipsoid, with theoretical guarantees on uniqueness, stability, and alignment with key feature directions. Empirically, ElliCE generates counterfactuals that are not only more robust but also more flexible, adapting to user-specified feature constraints while being substantially faster than existing baselines. This provides a principled and practical solution for reliable recourse under model uncertainty, ensuring stable recommendations for users even as models evolve.

翻译：机器学习模型如今直接影响人们生活的决策，因此不仅需要理解其预测结果，还需了解个体如何行动才能获得更优结果。算法追索通过提供可操作的输入修改方案来实现更有利的结果，通常依赖于反事实解释来建议此类变更。然而，当Rashomon集合（即近似最优模型集合）规模较大时，标准的反事实解释可能变得不可靠，因为对某个模型有效的追索行动在另一模型下可能失效。本文提出ElliCE这一新颖的鲁棒算法追索框架，通过在Rashomon集合的椭球近似上优化反事实解释。所得解释在该椭球范围内具有可证明的有效性，并在唯一性、稳定性以及与关键特征方向的对齐性方面提供理论保证。实验表明，ElliCE生成的反事实解释不仅更具鲁棒性，而且更灵活，能够适应用户指定的特征约束，同时计算速度显著优于现有基线方法。这为模型不确定性下的可靠追索提供了原则性与实用性兼备的解决方案，确保即使用户模型动态演进也能获得稳定的推荐建议。