# Stochastic Learning Approach to Binary Optimization for Optimal Design of Experiments

arXiv: https://arxiv.org/abs/2101.05958 · HTML: https://mlsanity.com/paper/2101.05958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 15 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion](https://mlsanity.com/paper/1308.1313/) (2013)
- [Optimal low-rank approximations of Bayesian linear inverse problems](https://mlsanity.com/paper/1407.3463/) (2014)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [A Fast and Scalable Method for A-Optimal Design of Experiments for Infinite-dimensional Bayesian Nonlinear Inverse Problems](https://mlsanity.com/paper/1410.5899/) (2014)
- [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](https://mlsanity.com/paper/1410.1221/) (2014)
- [Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction](https://mlsanity.com/paper/1510.06053/) (2015)
- [Fast Incremental Method for Nonconvex Optimization](https://mlsanity.com/paper/1603.06159/) (2016)
- [A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification](https://mlsanity.com/paper/1308.4084/) (2013)
- [hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference](https://mlsanity.com/paper/1909.03948/) (2019)
- [Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations](https://mlsanity.com/paper/2007.14476/) (2020)
- [Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs](https://mlsanity.com/paper/1912.08915/) (2019)
- [Optimal Experimental Design for Infinite-dimensional Bayesian Inverse Problems Governed by PDEs: A Review](https://mlsanity.com/paper/2005.12998/) (2020)

## Abstract (arXiv)

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.