Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Journal Article · Wed Apr 13 00:00:00 EDT 2022 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/21m1404363· OSTI ID:1909666

Attia, Ahmed ^[1]; Leyffer, Sven ^[1]; Munson, Todd S. ^[1]

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1. Argonne National Lab. (ANL), Lemont, IL (United States)

Here, we present a novel stochastic approach to binary optimization suited 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. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $$\ell_0$$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed 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.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 1909666
• Journal Information: SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 2 Vol. 44; ISSN 1064-8275
• Publisher: Society for Industrial and Applied Mathematics (SIAM)
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Bayesian inverse problem
Bayesian inversion
Binary optimization
Design of experiments
Reinforcement learning
Stochastic optimization