# Bounds on the Generalization Error in Active Learning

arXiv: https://arxiv.org/abs/2409.09078 · HTML: https://mlsanity.com/paper/2409.09078/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 10 Sep 2024.

## Builds on (most cited first, 5 of 5)

- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks](https://mlsanity.com/paper/1805.12076/) (2018)
- [Deep Active Learning: Unified and Principled Method for Query and Training](https://mlsanity.com/paper/1911.09162/) (2019)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)

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

- [A Mechanism-Driven Theory of Phase Transitions in Active Learning](https://mlsanity.com/paper/2607.00144/) (2026)

## Abstract (arXiv)

We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be obtained by combining both informativeness and representativeness query strategies, where the latter is assessed using integral probability metrics. To facilitate the use of these bounds in application, we systematically link diverse active learning scenarios, characterized by their loss functions and hypothesis classes to their corresponding upper bounds. Our results show that regularization techniques used to constraint the complexity of various hypothesis classes are sufficient conditions to ensure the validity of the bounds. The present work enables principled construction and empirical quality-evaluation of query algorithms in active learning.