$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks
Abstract
We propose and analyze StoROO, an algorithm for risk optimization on stochastic black-box functions derived from StoOO. Motivated by risk-averse decision making fields like agriculture, medicine, biology or finance, we do not focus on the mean payoff but on generic functionals of the return distribution. We provide a generic regret analysis of StoROO and illustrate its applicability with two examples: the optimization of quantiles and CVaR. Inspired by the bandit literature and black-box mean optimizers, StoROO relies on the possibility to construct confidence intervals for the targeted functional based on random-size samples. We detail their construction in the case of quantiles, providing tight bounds based on Kullback-Leibler divergence. We finally present numerical experiments that show a dramatic impact of tight bounds for the optimization of quantiles and CVaR.
Cite
Text
Torossian et al. "$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks." Proceedings of The Eleventh Asian Conference on Machine Learning, 2019.Markdown
[Torossian et al. "$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks." Proceedings of The Eleventh Asian Conference on Machine Learning, 2019.](https://mlanthology.org/acml/2019/torossian2019acml-xarmed/)BibTeX
@inproceedings{torossian2019acml-xarmed,
title = {{$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks}},
author = {Torossian, Léonard and Garivier, Aurélien and Picheny, Victor},
booktitle = {Proceedings of The Eleventh Asian Conference on Machine Learning},
year = {2019},
pages = {252-267},
volume = {101},
url = {https://mlanthology.org/acml/2019/torossian2019acml-xarmed/}
}