# A Survey of Feedback Particle Filter and related Controlled Interacting Particle Systems (CIPS)

arXiv: https://arxiv.org/abs/2301.00935 · HTML: https://mlsanity.com/paper/2301.00935/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2023.

## Built on by (most cited first, 5 of 5)

- [Sampling in Unit Time with Kernel Fisher-Rao Flow](https://mlsanity.com/paper/2401.03892/) (2024)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps](https://mlsanity.com/paper/2503.12633/) (2025)
- [Interacting Particle Systems for Fast Linear Quadratic RL](https://mlsanity.com/paper/2406.11057/) (2024)
- [Functional role of synchronization: A mean-field control perspective](https://mlsanity.com/paper/2502.00590/) (2025)

## Abstract (arXiv)

In this survey, we describe controlled interacting particle systems (CIPS) to approximate the solution of the optimal filtering and the optimal control problems. Part I of the survey is focussed on the feedback particle filter (FPF) algorithm, its derivation based on optimal transportation theory, and its relationship to the ensemble Kalman filter (EnKF) and the conventional sequential importance sampling-resampling (SIR) particle filters. The central numerical problem of FPF -- to approximate the solution of the Poisson equation -- is described together with the main solution approaches. An analytical and numerical comparison with the SIR particle filter is given to illustrate the advantages of the CIPS approach. Part II of the survey is focussed on adapting these algorithms for the problem of reinforcement learning. The survey includes several remarks that describe extensions as well as open problems in this subject.