Convergence acceleration of ensemble Kalman inversion in nonlinear settings

Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models involved, derivative-free optimization tools often needed. The ensemble Kalman filter (EnKF) is particle-based Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to computational efficiency. resulting algorithm, known inversion (EKI), involves running of particles with EnKF update rules so they converge minimizer. In this article, we investigate EKI convergence in general nonlinear settings. To improve speed and stability, consider applying non-constant step-sizes covariance inflation. We prove that hit critical points finite steps non-convex further converges global minimizer polynomially fast if function strongly convex. verify analysis presented numerical experiments on two problems.