# On Learning the Optimal Regularization Parameter in Inverse Problems

arXiv: https://arxiv.org/abs/2311.15845 · HTML: https://mlsanity.com/paper/2311.15845/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2023.

## Built on by (most cited first, 5 of 5)

- [Learning sparsity-promoting regularizers for linear inverse problems](https://mlsanity.com/paper/2412.16031/) (2024)
- [Learning Multi-Index Models with Hyper-Kernel Ridge Regression](https://mlsanity.com/paper/2510.02532/) (2025)
- [Statistical inverse learning problems with random observations](https://mlsanity.com/paper/2312.15341/) (2023)
- [Optimal Regularization Under Uncertainty: Distributional Robustness and Convexity Constraints](https://mlsanity.com/paper/2510.03464/) (2025)
- [On the Sample Complexity of Learning for Blind Inverse Problems](https://mlsanity.com/paper/2512.23405/) (2025)

## Abstract (arXiv)

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require less a priori knowledge, but their theoretical analysis is limited. In this paper, we propose and study a statistical machine learning approach, based on empirical risk minimization. Our main contribution is a theoretical analysis, showing that, provided with enough data, this approach can reach sharp rates while being essentially adaptive to the noise and smoothness of the problem. Numerical simulations corroborate and illustrate the theoretical findings. Our results are a step towards grounding theoretically data-driven approaches to inverse problems.