# Order-based Rehearsal Learning

arXiv: https://arxiv.org/abs/2605.04955 · HTML: https://mlsanity.com/paper/2605.04955/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Guided Image Generation with Conditional Invertible Neural Networks](https://mlsanity.com/paper/1907.02392/) (2019)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Causal Representation Learning from Multiple Distributions: A General Setting](https://mlsanity.com/paper/2402.05052/) (2024)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [Efficient multivariate entropy estimation via k-nearest neighbour distances](https://mlsanity.com/paper/1606.00304/) (2016)
- [Ordering-Based Causal Discovery for Linear and Nonlinear Relations](https://mlsanity.com/paper/2410.05890/) (2024)
- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)

## Built on by (most cited first, 1 of 1)

- [Non-Parametric Rehearsal Learning via Conditional Mean Embeddings](https://mlsanity.com/paper/2605.08999/) (2026)

## Abstract (arXiv)

When a machine learning (ML) model forecasts an undesired event, one often seeks a decision to avoid it, known as the avoiding undesired future (AUF) problem. Many rehearsal learning methods have been proposed for AUF, but they rely on an underlying graph structure; learning such a graph from observational data is challenging and can incur substantial estimation error. In this work, we demonstrate that the order structure can be sufficient for AUF decision-making, and propose the first order-based rehearsal learning method. Although an order is less informative than a graph, it can be sufficient to identify the influence of decisions from observational data, suggesting that learning the entire graph is not always necessary. To learn the order, we develop an information-theoretic method that imposes no restrictions on the form of structural functions or the type of noise distributions. For AUF decision-making, we construct an order-based sampler to approximate the influence of decisions and, combined with a surrogate objective for maximizing the post-decision success probability, reduce the AUF task to a differentiable optimization problem. Experiments show that our order learning method outperforms existing methods, and that our AUF approach not only surpasses methods relying on learned graphs or learned orders, but also matches or even exceeds oracle baselines that are given the true graph.