# Probabilistic Approach to Black-Box Binary Optimization with Budget Constraints: Application to Sensor Placement

arXiv: https://arxiv.org/abs/2406.05830 · HTML: https://mlsanity.com/paper/2406.05830/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 73 references that are in the map.
- First posted on arXiv 9 Jun 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning to Hash for Indexing Big Data - A Survey](https://mlsanity.com/paper/1509.05472/) (2015)
- [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)
- [Training Binary Neural Networks using the Bayesian Learning Rule](https://mlsanity.com/paper/2002.10778/) (2020)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [Constrained Discrete Black-Box Optimization using Mixed-Integer Programming](https://mlsanity.com/paper/2110.09569/) (2021)
- [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)
- [A-optimal design of experiments for infinite-dimensional Bayesian linear inverse problems with regularized ℓ0-sparsification](https://mlsanity.com/paper/1308.4084/) (2013)
- [Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations](https://mlsanity.com/paper/2007.14476/) (2020)
- [Heuristic Algorithms for Placing Geomagnetically Induced Current Blocking Devices](https://mlsanity.com/paper/2310.09409/) (2023)
- [Robust A-Optimal Experimental Design for Bayesian Inverse Problems](https://mlsanity.com/paper/2305.03855/) (2023)

## Built on by (most cited first, 1 of 1)

- [A Probabilistic Approach to Trajectory-Based Optimal Experimental Design](https://mlsanity.com/paper/2601.11473/) (2026)

## Abstract (arXiv)

This paper presents a fully probabilistic approach for solving optimal experimental design problems under budget constraints. The experimental design is viewed as a random variable and is associated with a parametric conditional distribution that inherently models the budget constraints. The original optimization problem is replaced with an optimization over the expected value of the original objective, which is then optimized over the distribution parameters. The resulting optimal parameter (policy) is used to sample the feasible region of binary space to produce estimates of the optimal solution(s) of the original optimization problem. In this work we extend the family of conditional Bernoulli models to model the random variable conditioned by the total number of nonzero entries, that is, the budget constraint. This approach (a) is generally applicable to binary optimization problems with nonstochastic black-box objective functions and budget constraints; (b) employs conditional probabilities to model and sample only the feasible region and thus considerably reduces the computational cost compared with employing soft constraints; and (c) does not employ soft constraints and thus does not require tuning of a regularization parameter, for example to promote sparsity, which is generally challenging. The proposed approach is verified numerically using an optimal sensor placement experiment based on an advection-diffusion forward model in a parameter identification setup.