Stochastic Learning Approach to Binary Optimization for Optimal Design of 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.

arXiv comment34 pages, 12 figures

References in corpus (10)

• SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives
• Simulation-based optimal Bayesian experimental design for nonlinear systems
• Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet
• Gradient-based stochastic optimization methods in Bayesian experimental design
• Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction
• Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems
• The Reduced-Order Hybrid Monte Carlo Sampling Smoother
• Fast Incremental Method for Nonconvex Optimization
• A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion
• Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Cited by in corpus (3)

• Robust optimal design of large-scale Bayesian nonlinear inverse problems
• Multifidelity sensor placement in Bayesian state estimation problems
• On the dual advantage of placing observations through forward sensitivity analysis