Argumentative Ensembling for Robust Recourse under Model Multiplicity

Abstract

In machine learning, it is common to obtain multiple equally performing models for the same prediction task, e.g., when training neural networks with different random seeds. Model multiplicity (MM) is the situation which arises when these competing models differ in their predictions for the same input, for which ensembling is often employed to determine an aggregation of the outputs. Providing recourse recommendations via counterfactual explanations (CEs) under MM thus becomes complex, since the CE may not be valid across all models, i.e., the CEs are not robust under MM. In this work, we formalise the problem of providing recourse under MM, which we name recourse-aware ensembling (RAE). We propose the idea that under MM, CEs for each individual model should be considered alongside their predictions so that the aggregated prediction and recourse are decided in tandem. Centred around this intuition, we introduce six desirable properties for solutions to this problem. For solving RAE, we propose a novel argumentative ensembling method which guarantees the robustness of CEs under MM. Specifically, our method leverages computational argumentation to explicitly represent the conflicts between models and counterfactuals regarding prediction results and CE validity. It then uses argumentation semantics to resolve the conflicts and obtain the final solution, in a manner which is parametric to the chosen semantics. Our method also allows for the specification of preferences over the models under MM, allowing further customisation of the ensemble. In a comprehensive theoretical analysis, we characterise the behaviour of argumentative ensembling with four different argumentation semantics. We then empirically demonstrate the effectiveness of our approach in satisfying desirable properties with eight instantiations of our method. (Abstract is shortened for arXiv.)