Nesterov Acceleration for Ensemble Kalman Inversion and Variants

TL;DR

This paper demonstrates that Nesterov acceleration can significantly speed up Ensemble Kalman Inversion (EKI) and its variants, providing a simple, hyperparameter-free method to enhance inverse problem solving without extra computational costs.

Contribution

It introduces a particle-level Nesterov acceleration technique for EKI and its variants, enabling faster convergence with minimal implementation complexity.

Findings

Nesterov acceleration speeds up EKI cost function reduction.

The method is easily integrated with existing EKI algorithms.

No additional computational cost or hyperparameters are required.

Abstract

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.