# Adaptive Preconditioned Gradient Descent with Energy

arXiv: https://arxiv.org/abs/2310.06733 · HTML: https://mlsanity.com/paper/2310.06733/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2023.

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

- [Accelerating Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2504.03158/) (2025)

## Abstract (arXiv)

We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as the Hessian-Riemannian and natural gradient descent methods. More specifically, we incorporate these preconditioned gradient descent algorithms in the recently introduced Adaptive Energy Gradient Descent (AEGD) framework. In particular, we discuss theoretical results on the unconditional energy-stability and convergence rates across three classes of objective functions. Furthermore, our numerical results demonstrate excellent performance of the proposed method on several test bed optimization problems.