preprint · arXiv (Cornell University) · 2016
Sequential Bayesian optimal experimental design via approximate dynamic programming
Cited by 38Open access
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.
Cite this paper
Huan, X., & Marzouk, Y. (2016). Sequential Bayesian optimal experimental design via approximate dynamic programming. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1604.08320
Huan, Xun, and Youssef Marzouk. “Sequential Bayesian optimal experimental design via approximate dynamic programming.” arXiv (Cornell University), 2016, https://doi.org/10.48550/arxiv.1604.08320.
Huan, Xun, and Youssef Marzouk. 2016. “Sequential Bayesian optimal experimental design via approximate dynamic programming.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1604.08320.
Huan, X. and Marzouk, Y. (2016) ‘Sequential Bayesian optimal experimental design via approximate dynamic programming’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1604.08320.
@misc{huan2016sequential,
title = {{Sequential Bayesian optimal experimental design via approximate dynamic programming}},
author = {Huan, Xun and Marzouk, Youssef},
journal = {arXiv (Cornell University)},
year = {2016},
doi = {10.48550/arxiv.1604.08320}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.