# An Optimization Approach to Learning Falling Rule Lists

arXiv: https://arxiv.org/abs/1710.02572 · HTML: https://mlsanity.com/paper/1710.02572/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2017.

## Built on by (most cited first, 10 of 10)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [SAT-Based Rigorous Explanations for Decision Lists](https://mlsanity.com/paper/2105.06782/) (2021)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [Quant-BnB: A Scalable Branch-and-Bound Method for Optimal Decision Trees with Continuous Features](https://mlsanity.com/paper/2206.11844/) (2022)
- [Learning Interpretable, High-Performing Policies for Autonomous Driving](https://mlsanity.com/paper/2202.02352/) (2022)
- [Finding Interpretable Class-Specific Patterns through Efficient Neural Search](https://mlsanity.com/paper/2312.04311/) (2023)
- [RGMDT: Return-Gap-Minimizing Decision Tree Extraction in Non-Euclidean Metric Space](https://mlsanity.com/paper/2410.16517/) (2024)
- [Fast Optimization of Weighted Sparse Decision Trees for use in Optimal Treatment Regimes and Optimal Policy Design](https://mlsanity.com/paper/2210.06825/) (2022)
- [Falling Trees: A Model Class for Interpretable Risk Prioritization](https://mlsanity.com/paper/2609.23780/) (2026)

## Abstract (arXiv)

A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a regular decision list, the order of rules in a falling rule list is important -- each example is classified by the first rule whose antecedent it satisfies. Unlike a regular decision list, a falling rule list requires the probabilities of the desired outcome ("1") to be monotonically decreasing down the list. We propose an optimization approach to learning falling rule lists and "softly" falling rule lists, along with Monte-Carlo search algorithms that use bounds on the optimal solution to prune the search space.