# Bayesian Optimization of Risk Measures

arXiv: https://arxiv.org/abs/2007.05554 · HTML: https://mlsanity.com/paper/2007.05554/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2020.

## Built on by (most cited first, 30 of 36)

- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Robust Multi-Objective Bayesian Optimization Under Input Noise](https://mlsanity.com/paper/2202.07549/) (2022)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Bayesian Optimization with High-Dimensional Outputs](https://mlsanity.com/paper/2106.12997/) (2021)
- [Thinking inside the box: A tutorial on grey-box Bayesian optimization](https://mlsanity.com/paper/2201.00272/) (2022)
- [qEUBO: A Decision-Theoretic Acquisition Function for Preferential Bayesian Optimization](https://mlsanity.com/paper/2303.15746/) (2023)
- [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)
- [Quantum Bayesian Optimization](https://mlsanity.com/paper/2310.05373/) (2023)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Bayesian Optimization of Function Networks with Partial Evaluations](https://mlsanity.com/paper/2311.02146/) (2023)
- [Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.13627/) (2022)
- [Batch Bayesian Optimization for Replicable Experimental Design](https://mlsanity.com/paper/2311.01195/) (2023)
- [BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertainty](https://mlsanity.com/paper/2510.03893/) (2025)
- [Two-step Lookahead Bayesian Optimization with Inequality Constraints](https://mlsanity.com/paper/2112.02833/) (2021)
- [On the Finite-Time Performance of the Knowledge Gradient Algorithm](https://mlsanity.com/paper/2206.06847/) (2022)
- [Multi-fidelity Machine Learning for Uncertainty Quantification and Optimization](https://mlsanity.com/paper/2410.23482/) (2024)
- [OPT-GAN: A Broad-Spectrum Global Optimizer for Black-box Problems by Learning Distribution](https://mlsanity.com/paper/2102.03888/) (2021)
- [Contextual Causal Bayesian Optimisation](https://mlsanity.com/paper/2301.12412/) (2023)
- [Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks](https://mlsanity.com/paper/2302.07260/) (2023)
- [Practical Bayesian Algorithm Execution via Posterior Sampling](https://mlsanity.com/paper/2410.20596/) (2024)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Bayesian Optimization of Expensive Nested Grey-Box Functions](https://mlsanity.com/paper/2306.05150/) (2023)
- [Learning-assisted Stochastic Capacity Expansion Planning: A Bayesian Optimization Approach](https://mlsanity.com/paper/2401.10451/) (2024)
- [Bayesian Optimization for Non-Convex Two-Stage Stochastic Optimization Problems](https://mlsanity.com/paper/2408.17387/) (2024)
- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)
- [Hyperparameter Optimization with Neural Network Pruning](https://mlsanity.com/paper/2205.08695/) (2022)
- [Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data](https://mlsanity.com/paper/2212.06253/) (2022)
- [Learning Relevant Contextual Variables Within Bayesian Optimization](https://mlsanity.com/paper/2305.14120/) (2023)

## Abstract (arXiv)

We consider Bayesian optimization of objective functions of the form ρ[ F(x, W) ], where F is a black-box expensive-to-evaluate function and ρ denotes either the VaR or CVaR risk measure, computed with respect to the randomness induced by the environmental random variable W. Such problems arise in decision making under uncertainty, such as in portfolio optimization and robust systems design. We propose a family of novel Bayesian optimization algorithms that exploit the structure of the objective function to substantially improve sampling efficiency. Instead of modeling the objective function directly as is typical in Bayesian optimization, these algorithms model F as a Gaussian process, and use the implied posterior on the objective function to decide which points to evaluate. We demonstrate the effectiveness of our approach in a variety of numerical experiments.