# MOSS: Multi-Objective Optimization for Stable Rule Sets

arXiv: https://arxiv.org/abs/2506.08030 · HTML: https://mlsanity.com/paper/2506.08030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [One Explanation Does Not Fit All: A Toolkit and Taxonomy of AI Explainability Techniques](https://mlsanity.com/paper/1909.03012/) (2019)
- [Exploring the Whole Rashomon Set of Sparse Decision Trees](https://mlsanity.com/paper/2209.08040/) (2022)
- [Veridical Data Science](https://mlsanity.com/paper/1901.08152/) (2019)
- [Generalized Linear Rule Models](https://mlsanity.com/paper/1906.01761/) (2019)
- [Sparse Classification: a scalable discrete optimization perspective](https://mlsanity.com/paper/1710.01352/) (2017)
- [Subset Selection with Shrinkage: Sparse Linear Modeling when the SNR is low](https://mlsanity.com/paper/1708.03288/) (2017)
- [L0Learn: A Scalable Package for Sparse Learning using L0 Regularization](https://mlsanity.com/paper/2202.04820/) (2022)
- [Computing the Collection of Good Models for Rule Lists](https://mlsanity.com/paper/2204.11285/) (2022)
- [Efficient Exploration of the Rashomon Set of Rule Set Models](https://mlsanity.com/paper/2406.03059/) (2024)
- [FIRE: An Optimization Approach for Fast Interpretable Rule Extraction](https://mlsanity.com/paper/2306.07432/) (2023)

## Abstract (arXiv)

We present MOSS, a multi-objective optimization framework for constructing stable sets of decision rules. MOSS incorporates three important criteria for interpretability: sparsity, accuracy, and stability, into a single multi-objective optimization framework. Importantly, MOSS allows a practitioner to rapidly evaluate the trade-off between accuracy and stability in sparse rule sets in order to select an appropriate model. We develop a specialized cutting plane algorithm in our framework to rapidly compute the Pareto frontier between these two objectives, and our algorithm scales to problem instances beyond the capabilities of commercial optimization solvers. Our experiments show that MOSS outperforms state-of-the-art rule ensembles in terms of both predictive performance and stability.