# Natural Variational Annealing for Multimodal Optimization

arXiv: https://arxiv.org/abs/2501.04667 · HTML: https://mlsanity.com/paper/2501.04667/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2025.

## Built on by (most cited first, 3 of 3)

- [Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixtures](https://mlsanity.com/paper/2602.12923/) (2026)
- [Natural Gradient VI: Guarantees for Non-Conjugate Models](https://mlsanity.com/paper/2510.19163/) (2025)
- [Leveraging generative models to assist Monte Carlo sampling](https://mlsanity.com/paper/2608.07648/) (2026)

## Abstract (arXiv)

We introduce a new multimodal optimization approach called Natural Variational Annealing (NVA) that combines the strengths of three foundational concepts to simultaneously search for multiple global and local modes of black-box nonconvex objectives. First, it implements a simultaneous search by using variational posteriors, such as, mixtures of Gaussians. Second, it applies annealing to gradually trade off exploration for exploitation. Finally, it learns the variational search distribution using natural-gradient learning where updates resemble well-known and easy-to-implement algorithms. The three concepts come together in NVA giving rise to new algorithms and also allowing us to incorporate "fitness shaping", a core concept from evolutionary algorithms. We assess the quality of search on simulations and compare them to methods using gradient descent and evolution strategies. We also provide an application to a real-world inverse problem in planetary science.