Value-at-Risk Optimization with Gaussian Processes

2021/05/13 by Quoc Phong Nguyen, Zhongxiang Dai, Nguyen, Quoc Phong +5 · 2 citations
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2105.06126

openalex publication_date 2021/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Value-at-risk (VaR) is an established measure to assess risks in critical real-world applications with random environmental factors. This paper presents a novel VaR upper confidence bound (V-UCB) algorithm for maximizing the VaR of a black-box objective function with the first no-regret guarantee. To realize this, we first derive a confidence bound of VaR and then prove the existence of values of the environmental random variable (to be selected to achieve no regret) such that the confidence bound of VaR lies within that of the objective function evaluated at such values. Our V-UCB algorithm empirically demonstrates state-of-the-art performance in optimizing synthetic benchmark functions, a portfolio optimization problem, and a simulated robot task.

Citations

• Max-value Entropy Search for Efficient Bayesian Optimization
• Adversarially Robust Optimization with Gaussian Processes

Cited by

• Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks
• Spectral Mixture Kernels for Bayesian Optimization

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