# Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design

arXiv: https://arxiv.org/abs/2409.05354 · HTML: https://mlsanity.com/paper/2409.05354/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 32 references that are in the map.
- First posted on arXiv 9 Sep 2024.

## Builds on (most cited first, 11 of 11)

- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Markovian Score Climbing: Variational Inference with KL(p||q)](https://mlsanity.com/paper/2003.10374/) (2020)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Sequential Bayesian optimal experimental design via approximate dynamic programming](https://mlsanity.com/paper/1604.08320/) (2016)
- [Particle Gibbs with Ancestor Sampling](https://mlsanity.com/paper/1401.0604/) (2014)
- [Nesting Particle Filters for Experimental Design in Dynamical Systems](https://mlsanity.com/paper/2402.07868/) (2024)
- [On backward smoothing algorithms](https://mlsanity.com/paper/2207.00976/) (2022)
- [State and parameter learning with PaRIS particle Gibbs](https://mlsanity.com/paper/2301.00900/) (2023)
- [Risk-Sensitive Stochastic Optimal Control as Rao-Blackwellized Markovian Score Climbing](https://mlsanity.com/paper/2312.14000/) (2023)

## Built on by (most cited first, 3 of 3)

- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Sequential Monte Carlo for Policy Optimization in Continuous POMDPs](https://mlsanity.com/paper/2505.16732/) (2025)
- [Online Bayesian Experimental Design for Partially Observed Dynamical Systems](https://mlsanity.com/paper/2511.04403/) (2025)

## Abstract (arXiv)

This paper introduces the Inside-Out Nested Particle Filter (IO-NPF), a novel, fully recursive, algorithm for amortized sequential Bayesian experimental design in the non-exchangeable setting. We frame policy optimization as maximum likelihood estimation in a non-Markovian state-space model, achieving (at most) O(T2) computational complexity in the number of experiments. We provide theoretical convergence guarantees and introduce a backward sampling algorithm to reduce trajectory degeneracy. IO-NPF offers a practical, extensible, and provably consistent approach to sequential Bayesian experimental design, demonstrating improved efficiency over existing methods.