Rashomon Sets of Falling Trees

Many real-world decisions require prioritizing high-risk cases, such as clinicians prioritizing high-risk patients before lower-risk ones. Falling rule lists (FRLs), which are ordered if--then rules with monotonically decreasing risks, provide an interpretable framework for such tasks; however, their single-path structure yields a highly restricted model class. We introduce falling trees, a new family of interpretable models that enforces the same monotonic risk constraint while permitting tree-structured branching. We present GraviTree, a novel dynamic-programming-with-bounds algorithm for learning the Rashomon set of falling trees under depth and branching constraints, together with bounds that use the falling constraint to provably reduce the search space. Our formulation can interpolate between rule lists and full decision trees, enabling user-desired model expressivity. Across clinical and public-risk datasets, falling trees match or outperform FRLs and other interpretable baselines, often producing lower-sparsity decisions for high-risk instances. Our results show that falling trees strike a practical balance between interpretability, expressiveness, and risk prioritization for high-stakes settings.