# PAC Learning is just Bipartite Matching (Sort of)

arXiv: https://arxiv.org/abs/2502.00607 · HTML: https://mlsanity.com/paper/2502.00607/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 2 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [A Characterization of Multiclass Learnability](https://mlsanity.com/paper/2203.01550/) (2022)
- [Optimal Learners for Multiclass Problems](https://mlsanity.com/paper/1405.2420/) (2014)
- [A Theory of PAC Learnability of Partial Concept Classes](https://mlsanity.com/paper/2107.08444/) (2021)
- [Optimal PAC Bounds Without Uniform Convergence](https://mlsanity.com/paper/2304.09167/) (2023)
- [From Local Pseudorandom Generators to Hardness of Learning](https://mlsanity.com/paper/2101.08303/) (2021)
- [Optimal Learners for Realizable Regression: PAC Learning and Online Learning](https://mlsanity.com/paper/2307.03848/) (2023)
- [On the Provable Advantage of Unsupervised Pretraining](https://mlsanity.com/paper/2303.01566/) (2023)
- [Adversarially Robust Learning: A Generic Minimax Optimal Learner and Characterization](https://mlsanity.com/paper/2209.07369/) (2022)
- [Learning local regularization for variational image restoration](https://mlsanity.com/paper/2102.06155/) (2021)
- [Regularization and Optimal Multiclass Learning](https://mlsanity.com/paper/2309.13692/) (2023)
- [Transductive Robust Learning Guarantees](https://mlsanity.com/paper/2110.10602/) (2021)
- [Suboptimality of Constrained Least Squares and Improvements via Non-Linear Predictors](https://mlsanity.com/paper/2009.09304/) (2020)
- [Improved Hardness Results for Learning Intersections of Halfspaces](https://mlsanity.com/paper/2402.15995/) (2024)
- [Is Transductive Learning Equivalent to PAC Learning?](https://mlsanity.com/paper/2405.05190/) (2024)
- [Is Efficient PAC Learning Possible with an Oracle That Responds 'Yes' or 'No'?](https://mlsanity.com/paper/2406.11667/) (2024)
- [Local Computation Algorithms for Graphs of Non-Constant Degrees](https://mlsanity.com/paper/1502.04022/) (2015)
- [Transductive Learning Is Compact](https://mlsanity.com/paper/2402.10360/) (2024)
- [Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples](https://mlsanity.com/paper/1907.05725/) (2019)

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

- [A One-Inclusion Graph Approach to Multi-Group Learning](https://mlsanity.com/paper/2603.23208/) (2026)

## Abstract (arXiv)

The main goal of this article is to convince you, the reader, that supervised learning in the Probably Approximately Correct (PAC) model is closely related to -- of all things -- bipartite matching! En-route from PAC learning to bipartite matching, I will overview a particular transductive model of learning, and associated one-inclusion graphs, which can be viewed as a generalization of some of the hat puzzles that are popular in recreational mathematics. Whereas this transductive model is far from new, it has recently seen a resurgence of interest as a tool for tackling deep questions in learning theory. A secondary purpose of this article could be as a (biased) tutorial on the connections between the PAC and transductive models of learning.