# Parametric Majorization for Data-Driven Energy Minimization Methods

## TL;DR

This paper introduces a new strategy for optimizing parametric energy minimization models by majorizing bi-level problems with surrogate single-level problems, enabling efficient training on large datasets.

## Contribution

It proposes a novel approach to handle bi-level optimization in energy minimization by using majorization, facilitating scalable and efficient training of data-driven models.

## Key findings

- Efficient algorithms for bi-level optimization problems.
- Framework enables training of parameterized energy models on large datasets.
- Maintains energy function integrity without collapse.

## Abstract

Energy minimization methods are a classical tool in a multitude of computer vision applications. While they are interpretable and well-studied, their regularity assumptions are difficult to design by hand. Deep learning techniques on the other hand are purely data-driven, often provide excellent results, but are very difficult to constrain to predefined physical or safety-critical models. A possible combination between the two approaches is to design a parametric energy and train the free parameters in such a way that minimizers of the energy correspond to desired solution on a set of training examples. Unfortunately, such formulations typically lead to bi-level optimization problems, on which common optimization algorithms are difficult to scale to modern requirements in data processing and efficiency. In this work, we present a new strategy to optimize these bi-level problems. We investigate surrogate single-level problems that majorize the target problems and can be implemented with existing tools, leading to efficient algorithms without collapse of the energy function. This framework of strategies enables new avenues to the training of parameterized energy minimization models from large data.