X -ARMED BANDITS: OPTIMIZING QUANTILES, CVAR AND OTHER RISKS

Léonard Torossian (1, 2) , Aurélien Garivier (3) , Victor Picheny (4)

1 MIAT INRA - Unité de Mathématiques et Informatique Appliquées de Toulouse
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
4 PROWLER.io, 72 Hills Road, Cambridge

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.

Mots clés: Optimistic optimization; Risk-averse solutions; Quantile optimization; CVaR optimization

Domaines: Statistiques [stat]; Machine Learning [stat.ML]

Léonard Torossian, Aurélien Garivier, Victor Picheny. X -ARMED BANDITS: OPTIMIZING QUANTILES, CVAR AND OTHER RISKS. Asian Conference on Machine Learning, Nov 2019, Nagoya, Japan. pp.252-267. ⟨hal-02101647v3⟩