  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.
