  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.
