# Bayesian Optimization of CVaR with Unknown Hyperparameters

arXiv: https://arxiv.org/abs/2610.18306 · HTML: https://mlsanity.com/paper/2610.18306/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (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)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [No-Regret Bayesian Optimization with Unknown Hyperparameters](https://mlsanity.com/paper/1901.03357/) (2019)
- [Bayesian Optimization of Risk Measures](https://mlsanity.com/paper/2007.05554/) (2020)
- [Value-at-Risk Optimization with Gaussian Processes](https://mlsanity.com/paper/2105.06126/) (2021)
- [Time-Varying Gaussian Process Bandits with Unknown Prior](https://mlsanity.com/paper/2402.01632/) (2024)
- [Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimal](https://mlsanity.com/paper/2410.10384/) (2024)
- [Adaptive Prior Selection in Gaussian Process Bandits with Thompson Sampling](https://mlsanity.com/paper/2502.01226/) (2025)
- [Bayesian Optimization for CVaR-based portfolio optimization](https://mlsanity.com/paper/2503.17737/) (2025)

## Abstract (arXiv)

We study Bayesian optimization of the Conditional Value-at-Risk (CVaR) of an expensive black-box function that depends on a decision and an environmental variable. Existing no-regret algorithms assume that the correct Gaussian process (GP) kernel and its hyperparameters are known. In practice, however, they must be estimated from limited data, often yielding a misspecified surrogate. This is especially damaging for CVaR because misspecification can distort the estimated tail-risk and thus lead to catastrophic decisions. We propose HE-CV-UCB, the first no-regret algorithm for CVaR Bayesian optimization with unknown GP hyperparameters. Given a finite candidate set containing a well-specified model, HE-CV-UCB adaptively eliminates those inconsistent with the observed data, actively queries where the survivors disagree, and returns a design that is robust across the surviving candidates. We prove that it attains cumulative regret matching the oracle rate of CV-UCB up to a factor depending only on the candidate set's size. Across synthetic benchmarks and three real-world applications, HE-CV-UCB achieves competitive performance and frequently outperforms existing CVaR Bayesian optimization methods.