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arXiv · 1904.08205

X-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks

Léonard Torossian·Aurélien Garivier·Victor Picheny
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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.

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Léonard Torossian, Aurélien Garivier, Victor Picheny. 2019-04-17. X-Armed Bandits: Optimizing Quantiles, CVaR and Other Risks. https://arxiv.org/abs/1904.08205

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