In this paper, we introduce the Ensemble Kalman-Stein Gradient Descent (EnKSGD) class of algorithms. The EnKSGD class of algorithms builds on the ensemble Kalman filter (EnKF) line of work, applying techniques from sequential data assimilation to unconstrained optimization and parameter estimation problems. The essential idea is to exploit the EnKF as a black box (i.e. derivative-free, zeroth order) optimization tool if iterated to convergence. In this paper, we return to the foundations of the EnKF as a sequential data assimilation technique, including its continuous-time and mean-field limits, with the goal of developing faster optimization algorithms suited to noisy black box optimization and inverse problems. The resulting EnKSGD class of algorithms can be designed to both maintain the desirable property of affine-invariance, and employ the well-known backtracking line search. Furthermore, EnKSGD algorithms are designed to not necessitate the subspace restriction property and variance collapse property of previous iterated EnKF approaches to optimization, as both these properties can be undesirable in an optimization context. EnKSGD also generalizes beyond the $L^{2}$ loss, and is thus applicable to a wider class of problems than the standard EnKF. Numerical experiments with both linear and nonlinear least squares problems, as well as maximum likelihood estimation, demonstrate the faster convergence of EnKSGD relative to alternative EnKF approaches to optimization.

翻译：本文介绍了集成卡尔曼-斯坦梯度下降（EnKSGD）算法类。EnKSGD算法类建立在集成卡尔曼滤波（EnKF）工作线之上，将顺序数据同化技术应用于无约束优化和参数估计问题。其核心思想是将EnKF作为黑箱（即无导数、零阶）优化工具，并在迭代收敛时加以利用。本文回归到EnKF作为顺序数据同化技术的基础，包括其连续时间极限和平均场极限，旨在开发适用于噪声黑箱优化和反问题的更快优化算法。所得到的EnKSGD算法类既能保持仿射不变性的理想性质，又能采用经典的回溯线搜索。此外，EnKSGD算法的设计无需已有迭代EnKF优化方法所要求的子空间限制性质和方差坍缩性质，因为这两种性质在优化背景下可能并不理想。EnKSGD还推广了$L^{2}$损失，适用于比标准EnKF更广泛的问题类别。针对线性和非线性最小二乘问题以及极大似然估计的数值实验表明，与替代的EnKF优化方法相比，EnKSGD具有更快的收敛速度。