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Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design

Sahel Iqbal, Hany Abdulsamad, Sara Pérez-Vieites, Simo Särkkä, Adrien Corenflos

TL;DR

The paper tackles efficient amortized Bayesian experimental design for non-exchangeable sequential data by introducing the Inside--Out Nested Particle Filter (IO--NPF), a fully recursive posterior-amortized approach. IO--NPF replaces the non-recursive IO--SMC2 with a jittering kernel and adds backward sampling, achieving provable consistency and reducing trajectory degeneracy to improve sample efficiency. Empirical validation on a stochastic pendulum demonstrates that IO--NPF with backward sampling yields higher realized information gain and better runtime trade-offs than IO--SMC2 and baselines, highlighting practical impact for real-time adaptive experiments. Limitations include the need for a Markovian outcome-likelihood, with future work aiming at non-asymptotic error bounds and stability guarantees for backward sampling.

Abstract

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) $\mathcal{O}(T^2)$ 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.

Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design

TL;DR

The paper tackles efficient amortized Bayesian experimental design for non-exchangeable sequential data by introducing the Inside--Out Nested Particle Filter (IO--NPF), a fully recursive posterior-amortized approach. IO--NPF replaces the non-recursive IO--SMC2 with a jittering kernel and adds backward sampling, achieving provable consistency and reducing trajectory degeneracy to improve sample efficiency. Empirical validation on a stochastic pendulum demonstrates that IO--NPF with backward sampling yields higher realized information gain and better runtime trade-offs than IO--SMC2 and baselines, highlighting practical impact for real-time adaptive experiments. Limitations include the need for a Markovian outcome-likelihood, with future work aiming at non-asymptotic error bounds and stability guarantees for backward sampling.

Abstract

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) 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.
Paper Structure (16 sections, 4 theorems, 39 equations, 1 figure, 5 tables, 4 algorithms)

This paper contains 16 sections, 4 theorems, 39 equations, 1 figure, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. The Dual Inference Problem
  4. The Inside--Out Nested Particle Filter (IO--NPF)
  5. Backward Sampling
  6. Numerical Validation
  7. Outlook and future work
  8. Individual Contributions
  9. Details of the Inside--Out NPF
  10. Target distribution of the IO--NPF
  11. Backward sampling
  12. Proof of Proposition \ref{['prop:consistency']}
  13. Details on Policy Amortization
  14. Details of Numerical Validation
  15. Stochastic pendulum environment
  16. ...and 1 more sections

Key Result

Proposition 1

Let $\Gamma_t^M(z_{0:t})$ denote the marginal target distribution of Algorithm alg:io-npf. Under technical conditions listed in Appendix app:prop-proof, for all bounded functions $h$, we have

Figures (1)

  • Figure 1: Accumulation of the realized information gain computed in closed form for different policies on the conditionally linear stochastic pendulum with a Gaussian parameter prior. We report the mean and standard deviation over $1024$ realizations. Here IO--SMC2 (Exact) \ref{['leg:io-smc2-exact']} represents an ideal baseline where $\theta$--posterior updates are closed-form, which is only possible in conjugate settings. Otherwise, our IO--NPF with backward sampling (BS) \ref{['leg:io-npf-bs']} outperforms all alternatives.

Theorems & Definitions (8)

  • Proposition 1: Consistency
  • Remark
  • Proposition 2
  • proof
  • Corollary 1
  • proof
  • Proposition 3: Consistency
  • proof