# Bayesian Optimization for Distributionally Robust Chance-constrained Problem

arXiv: https://arxiv.org/abs/2201.13112 · HTML: https://mlsanity.com/paper/2201.13112/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 36 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 16 of 16)

- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [A General Framework for Constrained Bayesian Optimization using Information-based Search](https://mlsanity.com/paper/1511.09422/) (2015)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [On Distributionally Robust Chance Constrained Programs with Wasserstein Distance](https://mlsanity.com/paper/1806.07418/) (2018)
- [Robust Super-Level Set Estimation using Gaussian Processes](https://mlsanity.com/paper/1811.09977/) (2018)
- [Distributionally Robust Bayesian Quadrature Optimization](https://mlsanity.com/paper/2001.06814/) (2020)
- [Bayesian Experimental Design for Finding Reliable Level Set under Input Uncertainty](https://mlsanity.com/paper/1910.12043/) (2019)
- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Active learning for level set estimation under input uncertainty and its extensions](https://mlsanity.com/paper/1909.06064/) (2019)
- [Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty under Wasserstein Ambiguity](https://mlsanity.com/paper/2003.12685/) (2020)
- [Bayesian Quadrature Optimization for Probability Threshold Robustness Measure](https://mlsanity.com/paper/2006.11986/) (2020)
- [A sampling criterion for constrained Bayesian optimization with uncertainties](https://mlsanity.com/paper/2103.05706/) (2021)

## Built on by (most cited first, 5 of 5)

- [Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds](https://mlsanity.com/paper/2302.01511/) (2023)
- [Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty](https://mlsanity.com/paper/2301.11588/) (2023)
- [Regret Analysis for Randomized Gaussian Process Upper Confidence Bound](https://mlsanity.com/paper/2409.00979/) (2024)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption](https://mlsanity.com/paper/2605.30089/) (2026)

## Abstract (arXiv)

In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.