用尼斯特罗夫加速改进集成卡尔曼反演，提升收敛速度。
Nesterov Acceleration for Ensemble Kalman Inversion and Variants
- 在粒子层面引入简单扰动实现加速，无需额外参数
- 在多种反问题上显著降低目标函数值
- 适配性强，可无缝集成到现有算法中
集成卡尔曼反演（EKI）是一种无梯度、基于粒子的优化方法，用于求解反问题。研究表明，EKI近似于梯度流，因此可应用加速梯度下降的方法。本文证明，尼斯特罗夫加速能有效加快多种反问题中EKI目标函数的下降速度。我们还将该加速方法应用于两种变体：无迹卡尔曼反演和集成变换卡尔曼反演。具体实现为粒子级扰动，具有黑箱耦合性，不增加计算开销，也不需要额外调参。本工作为将梯度优化的进展迁移到无梯度卡尔曼优化提供了新路径。
原文摘要 · Abstract (English)
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.
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