Phase-Alternation and Tree-Initialization to Facilitate Interpretable Rule-based Machine Learning

Interpretable machine learning is important for scientific, biomedical, and other high-stakes domains where transparency, trust, and human understanding of models are required. Recently, an evolutionary rule-based machine learning algorithm called HEROS was proposed, which separated rule from rule-set discovery each with distinct multi-objective optimization strategies yielding a two-phase, noise agnostic framework that found accurate, highly compact, and interpretable solutions on a diverse set of challenging benchmarks without requiring hyperparameter optimizations. However, HEROS is currently limited by its strictly sequential two-phase design which requires committing in advance to a fixed number of rule-discovery iterations. This work extends HEROS with a phase alternation scheme interleaving rule discovery and rule-set optimization. This enables refinement of both tasks throughout training in an 'anytime-algorithm' manner. We also introduce a tree-based rule initialization strategy to accelerate early-stage rule discovery. These extensions aim to preserve the empirical performance of the original HEROS framework under a similar computational budget while providing greater flexibility for algorithm application and problem scalability. Using the same diverse set of benchmark datasets, we evaluate and compare these HEROS extensions to the original HEROS algorithm and established rule-based learning systems including RIPPER and BioHEL. We demonstrate the advantages of this extended HEROS framework.