Nesterov Acceleration for Ensemble Kalman Inversion and Variants
This incremental improvement benefits researchers and practitioners in computational science and engineering by enhancing optimization efficiency in gradient-free methods.
The authors tackled the problem of slow convergence in ensemble Kalman inversion (EKI) methods for inverse problems by applying Nesterov acceleration, which sped up cost function reduction without extra computational cost or hyperparameters.
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.