Rule-based Machine Learning: Separating Rule and Rule-Set Pareto-Optimization for Interpretable Noise-Agnostic...

Rule-based machine learning (RBML) algorithms, e.g. learning classifier systems (LCSs), can capture complex relationships while yielding more interpretable models than most other machine learning algorithms. Traditional LCSs rely on a single fitness function for both rule and/or rule-set optimization. However, ideal rule vs. rule-set discovery often requires distinct and multiple objectives. Recently, hybrid-LCSs were proposed that explicitly separated the task of rule vs. rule-set discovery but relied on distinct single-objective or weighted multi-objective fitness functions. This study introduces a newly developed Heuristic Evolutionary Rule Optimization System (HEROS) that combines previous LCS innovations aimed at tackling noisy, larger-scale, classification tasks, while adopting separation of rule vs. rule-set evolution. Uniquely, HEROS employs a custom Pareto-front-based multi-objective fitness function (for rule discovery) and NSGA-II-style multi-objective optimization (for rule-set discovery) to solve both clean and noisy-signal classification problems agnostically. Rule discovery is driven by rule-accuracy and instance coverage objectives, while rule-set discovery is driven by prediction accuracy and rule-set size objectives. Using diverse simulated benchmark datasets, i.e. noisy (GAMETES) and clean (MUX), we demonstrate proof-of-principle that HEROS can directly discover accurate, highly-compact, interpretable, and ideal solutions when compared to the established 'ExSTraCS' RBML algorithm, without objective weightings or adjusting hyperparameters.