# Distributionally Robust Bayesian Optimization

arXiv: https://arxiv.org/abs/2002.09038 · HTML: https://mlsanity.com/paper/2002.09038/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

## Built on by (most cited first, 30 of 61)

- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Unsupervised Learning of Debiased Representations with Pseudo-Attributes](https://mlsanity.com/paper/2108.02943/) (2021)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Are Random Decompositions all we need in High Dimensional Bayesian Optimisation?](https://mlsanity.com/paper/2301.12844/) (2023)
- [Data-Driven Offline Decision-Making via Invariant Representation Learning](https://mlsanity.com/paper/2211.11349/) (2022)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [Automatic Termination for Hyperparameter Optimization](https://mlsanity.com/paper/2104.08166/) (2021)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Near-Optimal Algorithms for Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2212.13669/) (2022)
- [Distributionally Robust Model-based Reinforcement Learning with Large State Spaces](https://mlsanity.com/paper/2309.02236/) (2023)
- [Distributionally Robust Bayesian Optimization with varphi-divergences](https://mlsanity.com/paper/2203.02128/) (2022)
- [Combining Pessimism with Optimism for Robust and Efficient Model-Based Deep Reinforcement Learning](https://mlsanity.com/paper/2103.10369/) (2021)
- [Bias-Robust Bayesian Optimization via Dueling Bandits](https://mlsanity.com/paper/2105.11802/) (2021)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Active learning for distributionally robust level-set estimation](https://mlsanity.com/paper/2102.04000/) (2021)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Robust Bandit Learning with Imperfect Context](https://mlsanity.com/paper/2102.05018/) (2021)
- [Designing Fiduciary Artificial Intelligence](https://mlsanity.com/paper/2308.02435/) (2023)
- [Movement Penalized Bayesian Optimization with Application to Wind Energy Systems](https://mlsanity.com/paper/2210.08087/) (2022)
- [Near-optimal Policy Identification in Active Reinforcement Learning](https://mlsanity.com/paper/2212.09510/) (2022)
- [Robust Generalization despite Distribution Shift via Minimum Discriminating Information](https://mlsanity.com/paper/2106.04443/) (2021)
- [Expert-Calibrated Learning for Online Optimization with Switching Costs](https://mlsanity.com/paper/2204.08572/) (2022)
- [Bayesian Optimization for Distributionally Robust Chance-constrained Problem](https://mlsanity.com/paper/2201.13112/) (2022)
- [Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty](https://mlsanity.com/paper/2301.11588/) (2023)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [Distributionally Robust Optimization with Markovian Data](https://mlsanity.com/paper/2106.06741/) (2021)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)

## Abstract (arXiv)

Robustness to distributional shift is one of the key challenges of contemporary machine learning. Attaining such robustness is the goal of distributionally robust optimization, which seeks a solution to an optimization problem that is worst-case robust under a specified distributional shift of an uncontrolled covariate. In this paper, we study such a problem when the distributional shift is measured via the maximum mean discrepancy (MMD). For the setting of zeroth-order, noisy optimization, we present a novel distributionally robust Bayesian optimization algorithm (DRBO). Our algorithm provably obtains sub-linear robust regret in various settings that differ in how the uncertain covariate is observed. We demonstrate the robust performance of our method on both synthetic and real-world benchmarks.