2019-10-15-torossian19a.md

title	crossref	abstract	layout	series	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	publisher	container-title	volume	genre	issued	pdf	extras
$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks	acml19	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.	inproceedings	Proceedings of Machine Learning Research	torossian19a	0	$\mathcal{X}$-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks	252	267	252-267	252	false	Torossian, L\'eonard and Garivier, Aur\'elien and Picheny, Victor	given family Léonard Torossian given family Aurélien Garivier given family Victor Picheny	2019-10-15		PMLR	Proceedings of The Eleventh Asian Conference on Machine Learning	101	inproceedings	date-parts 2019 10 15	http://proceedings.mlr.press/v101/torossian19a/torossian19a.pdf	label link Supplementary PDF http://proceedings.mlr.press/v101/torossian19a/torossian19a-supp.pdf