Nesterov Acceleration for Ensemble Kalman Inversion and Variants

Fuente: arXiv
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Auteurs principaux: Vernon, Sydney, Bach, Eviatar, Dunbar, Oliver R. A.
Format: Preprint
Publié: 2025
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author Vernon, Sydney
Bach, Eviatar
Dunbar, Oliver R. A.
author_facet Vernon, Sydney
Bach, Eviatar
Dunbar, Oliver R. A.
contents Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.
format Preprint
id arxiv_https___arxiv_org_abs_2501_08779
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Nesterov Acceleration for Ensemble Kalman Inversion and Variants
Vernon, Sydney
Bach, Eviatar
Dunbar, Oliver R. A.
Optimization and Control
Machine Learning
Computation
Ensemble Kalman inversion (EKI) is a derivative-free, particle-based optimization method for solving inverse problems. It can be shown that EKI approximates a gradient flow, which allows the application of methods for accelerating gradient descent. Here, we show that Nesterov acceleration is effective in speeding up the reduction of the EKI cost function on a variety of inverse problems. We also implement Nesterov acceleration for two EKI variants, unscented Kalman inversion and ensemble transform Kalman inversion. Our specific implementation takes the form of a particle-level nudge that is demonstrably simple to couple in a black-box fashion with any existing EKI variant algorithms, comes with no additional computational expense, and with no additional tuning hyperparameters. This work shows a pathway for future research to translate advances in gradient-based optimization into advances in gradient-free Kalman optimization.
title Nesterov Acceleration for Ensemble Kalman Inversion and Variants
topic Optimization and Control
Machine Learning
Computation
url https://arxiv.org/abs/2501.08779