Sequential Bayesian optimal experimental design via approximate dynamic programming

TL;DR

This paper develops new Bayesian sequential experimental design strategies using approximate dynamic programming, enabling more effective and adaptive experiment planning compared to traditional batch or greedy methods.

Contribution

It formulates the sOED problem as a dynamic program, introduces numerical approaches for nonlinear design, and demonstrates improved performance over existing methods.

Findings

Verified against analytical solutions in linear-Gaussian models

Demonstrated advantages on nonlinear source inversion problems

Developed iterative algorithms for policy approximation

Abstract

The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formulate the general sequential optimal experimental design (sOED) problem as a dynamic program. Batch and greedy designs are shown to result from special cases of this formulation. We then focus on sOED for parameter inference, adopting a Bayesian formulation with an information theoretic design objective. To make the problem tractable, we develop new numerical approaches for nonlinear design with continuous parameter, design, and observation spaces. We approximate the optimal policy by using backward induction with regression to construct and refine value function approximations in the dynamic program. The proposed algorithm iteratively generates trajectories via exploration and exploitation to improve approximation accuracy in frequently visited regions of the state space. Numerical results are verified against analytical solutions in a linear-Gaussian setting. Advantages over batch and greedy design are then demonstrated on a nonlinear source inversion problem where we seek an optimal policy for sequential sensing.