# Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems

arXiv: https://arxiv.org/abs/2408.17387 · HTML: https://mlsanity.com/paper/2408.17387/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 71 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 20 of 20)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [The reparameterization trick for acquisition functions](https://mlsanity.com/paper/1712.00424/) (2017)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Bayesian Optimization with Expensive Integrands](https://mlsanity.com/paper/1803.08661/) (2018)
- [Noisy-Input Entropy Search for Efficient Robust Bayesian Optimization](https://mlsanity.com/paper/2002.02820/) (2020)
- [A supermartingale approach to Gaussian process based sequential design of experiments](https://mlsanity.com/paper/1608.01118/) (2016)
- [Unscented Bayesian Optimization for Safe Robot Grasping](https://mlsanity.com/paper/1603.02038/) (2016)
- [Bayesian optimisation under uncertain inputs](https://mlsanity.com/paper/1902.07908/) (2019)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Bayesian Optimization Allowing for Common Random Numbers](https://mlsanity.com/paper/1910.09259/) (2019)
- [Bayesian Optimisation for Constrained Problems](https://mlsanity.com/paper/2105.13245/) (2021)
- [Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluations](https://mlsanity.com/paper/2302.01310/) (2023)
- [Knowledge Gradient for Selection with Covariates: Consistency and Computation](https://mlsanity.com/paper/1906.05098/) (2019)
- [Efficient computation of the Knowledge Gradient for Bayesian Optimization](https://mlsanity.com/paper/2209.15367/) (2022)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [Joint Optimization of Wind Farm Layout Considering Optimal Control](https://mlsanity.com/paper/2107.11620/) (2021)
- [An Overview of Uncertain Control Co-Design Formulations](https://mlsanity.com/paper/2302.05491/) (2023)

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

- [Maximizing Reliability with Bayesian Optimization](https://mlsanity.com/paper/2602.02432/) (2026)

## Abstract (arXiv)

Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In the first stage of a two-stage problem, here-and-now decisions must be made in the face of uncertainty, while in the second stage, wait-and-see decisions are made after the uncertainty has been resolved. Many methods in stochastic programming assume that the objective is cheap to evaluate and linear or convex. We apply Bayesian optimization to solve non-convex, two-stage stochastic programs which are black-box and expensive to evaluate as, for example, is often the case with simulation objectives. We formulate a knowledge-gradient-based acquisition function to jointly optimize the first- and second-stage variables, establish a guarantee of asymptotic consistency, and provide a computationally efficient approximation. We demonstrate comparable empirical results to an alternative we formulate with fewer approximations, which alternates its focus between the two variable types, and superior empirical results over the state of the art and the standard, na"ive, two-step benchmark.