# Convergence rates for critical point regularization

arXiv: https://arxiv.org/abs/2302.08830 · HTML: https://mlsanity.com/paper/2302.08830/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation](https://mlsanity.com/paper/2402.01052/) (2024)
- [Convergence analysis of equilibrium methods for inverse problems](https://mlsanity.com/paper/2306.01421/) (2023)

## Abstract (arXiv)

Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained neural networks, has been shown to be effective in many cases. However, finding global minimizers in non-convex situations can be challenging, making existing theory inapplicable. A recent development in regularization theory relaxes this requirement by providing convergence based on critical points instead of strict minimizers. This paper investigates convergence rates for the regularization with critical points using Bregman distances. Furthermore, we show that when implementing near-minimization through an iterative algorithm, a finite number of iterations is sufficient without affecting convergence rates.