Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments

TL;DR

This paper introduces a stochastic optimization method for binary decision problems in experimental design, leveraging policy gradient techniques and Bayesian inverse problem frameworks to optimize sensor placement.

Contribution

It develops a novel stochastic approach for binary optimization in experimental design, connecting it with reinforcement learning and demonstrating its effectiveness through numerical experiments.

Findings

Effective sensor placement in Bayesian inverse problems.

The stochastic method outperforms traditional approaches.

Validation through extensive numerical experiments.

Abstract

We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. The proposed approach is analyzed from an optimization perspective and also from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem, and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.