Value-at-Risk Optimization with Gaussian Processes

Quoc Phong Nguyen, Zhongxiang Dai, Bryan Kian Hsiang Low, Patrick Jaillet
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:8063-8072, 2021.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-nguyen21b, title = {Value-at-Risk Optimization with Gaussian Processes}, author = {Nguyen, Quoc Phong and Dai, Zhongxiang and Low, Bryan Kian Hsiang and Jaillet, Patrick}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {8063--8072}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/nguyen21b/nguyen21b.pdf}, url = {https://proceedings.mlr.press/v139/nguyen21b.html}, 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.} }
Endnote
%0 Conference Paper %T Value-at-Risk Optimization with Gaussian Processes %A Quoc Phong Nguyen %A Zhongxiang Dai %A Bryan Kian Hsiang Low %A Patrick Jaillet %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-nguyen21b %I PMLR %P 8063--8072 %U https://proceedings.mlr.press/v139/nguyen21b.html %V 139 %X 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.
APA
Nguyen, Q.P., Dai, Z., Low, B.K.H. & Jaillet, P.. (2021). Value-at-Risk Optimization with Gaussian Processes. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:8063-8072 Available from https://proceedings.mlr.press/v139/nguyen21b.html.

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