# Constrained Machine Learning: The Bagel Framework

arXiv: https://arxiv.org/abs/2112.01088 · HTML: https://mlsanity.com/paper/2112.01088/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [Teaching the Old Dog New Tricks: Supervised Learning with Constraints](https://mlsanity.com/paper/2002.10766/) (2020)
- [Compact-Table: Efficiently Filtering Table Constraints with Reversible Sparse Bit-Sets](https://mlsanity.com/paper/1604.06641/) (2016)
- [Local Propagation in Constraint-based Neural Network](https://mlsanity.com/paper/2002.07720/) (2020)

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

- [Data-Centric Approach to Constrained Machine Learning: A Case Study on Conway's Game of Life](https://mlsanity.com/paper/2408.12778/) (2024)

## Abstract (arXiv)

Machine learning models are widely used for real-world applications, such as document analysis and vision. Constrained machine learning problems are problems where learned models have to both be accurate and respect constraints. For continuous convex constraints, many works have been proposed, but learning under combinatorial constraints is still a hard problem. The goal of this paper is to broaden the modeling capacity of constrained machine learning problems by incorporating existing work from combinatorial optimization. We propose first a general framework called BaGeL (Branch, Generate and Learn) which applies Branch and Bound to constrained learning problems where a learning problem is generated and trained at each node until only valid models are obtained. Because machine learning has specific requirements, we also propose an extended table constraint to split the space of hypotheses. We validate the approach on two examples: a linear regression under configuration constraints and a non-negative matrix factorization with prior knowledge for latent semantics analysis.