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
@article{arxiv.1904.08205,
title = {X-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks},
author = {Léonard Torossian and Aurélien Garivier and Victor Picheny},
journal= {arXiv preprint arXiv:1904.08205},
year = {2020}
}