Recursive Nested Filtering for Efficient Amortized Bayesian Experimental Design

TL;DR

This paper presents IO-NPF, a recursive algorithm for efficient, amortized Bayesian experimental design with theoretical guarantees and reduced degeneracy, improving over existing methods.

Contribution

It introduces the Inside-Out Nested Particle Filter, a novel recursive approach with convergence guarantees for sequential Bayesian experimental design.

Findings

Achieves at most quadratic computational complexity in the number of experiments.

Provides theoretical convergence guarantees.

Demonstrates improved efficiency over existing methods.

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.