Towards Robustness and Explainability of Automatic Algorithm Selection

Algorithm selection aims to identify the optimal performing algorithm before execution. Existing techniques typically focus on the observed correlations between algorithm performance and meta-features. However, little research has explored the underlying mechanisms of algorithm selection, specifically what characteristics an algorithm must possess to effectively tackle problems with certain feature values. This gap not only limits the explainability but also makes existing models vulnerable to data bias and distribution shift. This paper introduces directed acyclic graph (DAG) to describe this mechanism, proposing a novel modeling paradigm that aligns more closely with the fundamental logic of algorithm selection. By leveraging DAG to characterize the algorithm feature distribution conditioned on problem features, our approach enhances robustness against marginal distribution changes and allows for finergrained predictions through the reconstruction of optimal algorithm features, with the final decision relying on differences between reconstructed and rejected algorithm features. Furthermore, we demonstrate that, the learned graph and the proposed counterfactual calculations offer our approach with both model-level and instance-level explainability.