Natural Variational Annealing for Multimodal Optimization

TL;DR

Natural Variational Annealing (NVA) is a novel optimization method that combines variational posteriors, annealing, and natural-gradient learning to effectively find multiple solutions in complex black-box problems, with applications demonstrated in simulations and planetary science.

Contribution

The paper introduces NVA, a new multimodal optimization algorithm that integrates three foundational concepts, enabling efficient search for multiple optima in nonconvex objectives.

Findings

NVA effectively finds multiple global and local modes.

NVA outperforms gradient descent and evolution strategies in simulations.

NVA successfully applied to a real-world planetary science inverse problem.

Abstract

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.