# Risk-averse Heteroscedastic Bayesian Optimization

arXiv: https://arxiv.org/abs/2111.03637 · HTML: https://mlsanity.com/paper/2111.03637/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 5 Nov 2021.

## Builds on (most cited first, 21 of 21)

- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [ChemBO: Bayesian Optimization of Small Organic Molecules with Synthesizable Recommendations](https://mlsanity.com/paper/1908.01425/) (2019)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Bayesian Optimization in AlphaGo](https://mlsanity.com/paper/1812.06855/) (2018)
- [BOSS: Bayesian Optimization over String Spaces](https://mlsanity.com/paper/2010.00979/) (2020)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Corruption-Tolerant Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2003.01971/) (2020)
- [Automatic LQR Tuning Based on Gaussian Process Global Optimization](https://mlsanity.com/paper/1605.01950/) (2016)
- [Replication or exploration? Sequential design for stochastic simulation experiments](https://mlsanity.com/paper/1710.03206/) (2017)
- [Bayesian Optimization for Synthetic Gene Design](https://mlsanity.com/paper/1505.01627/) (2015)
- [Bayesian Optimization under Heavy-tailed Payoffs](https://mlsanity.com/paper/1909.07040/) (2019)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)
- [Distributionally Robust Bayesian Quadrature Optimization](https://mlsanity.com/paper/2001.06814/) (2020)
- [Mixed Strategies for Robust Optimization of Unknown Objectives](https://mlsanity.com/paper/2002.12613/) (2020)

## Built on by (most cited first, 17 of 17)

- [Bayesian Optimization with Conformal Prediction Sets](https://mlsanity.com/paper/2210.12496/) (2022)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Likelihood Ratio Confidence Sets for Sequential Decision Making](https://mlsanity.com/paper/2311.04402/) (2023)
- [Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimation](https://mlsanity.com/paper/2307.13371/) (2023)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [Bounding Box-based Multi-objective Bayesian Optimization of Risk Measures under Input Uncertainty](https://mlsanity.com/paper/2301.11588/) (2023)
- [Adversarial Causal Bayesian Optimization](https://mlsanity.com/paper/2307.16625/) (2023)
- [Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraints](https://mlsanity.com/paper/2310.08751/) (2023)
- [Batched Energy-Entropy acquisition for Bayesian Optimization](https://mlsanity.com/paper/2410.08804/) (2024)
- [Safe Bayesian optimization across noise models via scenario programming](https://mlsanity.com/paper/2512.11580/) (2025)
- [Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data](https://mlsanity.com/paper/2212.06253/) (2022)
- [Applications of Gaussian Processes at Extreme Lengthscales: From Molecules to Black Holes](https://mlsanity.com/paper/2303.14291/) (2023)
- [A Comparative Study of Hyperparameter Tuning Methods](https://mlsanity.com/paper/2408.16425/) (2024)
- [Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions](https://mlsanity.com/paper/2409.12622/) (2024)
- [Why risk matters for protein binder design](https://mlsanity.com/paper/2504.00146/) (2025)
- [No-Regret Gaussian Process Optimization of Time-Varying Functions](https://mlsanity.com/paper/2512.00517/) (2025)
- [Efficient Heteroscedastic Bayesian Optimization for Risk-Aware AutoRL](https://mlsanity.com/paper/2607.26680/) (2026)

## Abstract (arXiv)

Many black-box optimization tasks arising in high-stakes applications require risk-averse decisions. The standard Bayesian optimization (BO) paradigm, however, optimizes the expected value only. We generalize BO to trade mean and input-dependent variance of the objective, both of which we assume to be unknown a priori. In particular, we propose a novel risk-averse heteroscedastic Bayesian optimization algorithm (RAHBO) that aims to identify a solution with high return and low noise variance, while learning the noise distribution on the fly. To this end, we model both expectation and variance as (unknown) RKHS functions, and propose a novel risk-aware acquisition function. We bound the regret for our approach and provide a robust rule to report the final decision point for applications where only a single solution must be identified. We demonstrate the effectiveness of RAHBO on synthetic benchmark functions and hyperparameter tuning tasks.