The Annals of Statistics

Optimal learning with Q-aggregation

Guillaume Lecué and Philippe Rigollet

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We consider a general supervised learning problem with strongly convex and Lipschitz loss and study the problem of model selection aggregation. In particular, given a finite dictionary functions (learners) together with the prior, we generalize the results obtained by Dai, Rigollet and Zhang [Ann. Statist. 40 (2012) 1878–1905] for Gaussian regression with squared loss and fixed design to this learning setup. Specifically, we prove that the $Q$-aggregation procedure outputs an estimator that satisfies optimal oracle inequalities both in expectation and with high probability. Our proof techniques somewhat depart from traditional proofs by making most of the standard arguments on the Laplace transform of the empirical process to be controlled.

Article information

Ann. Statist., Volume 42, Number 1 (2014), 211-224.

First available in Project Euclid: 18 February 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 68Q32: Computational learning theory [See also 68T05]
Secondary: 62G08: Nonparametric regression 62G05: Estimation

Learning theory empirical risk minimization aggregation empirical processes theory


Lecué, Guillaume; Rigollet, Philippe. Optimal learning with Q -aggregation. Ann. Statist. 42 (2014), no. 1, 211--224. doi:10.1214/13-AOS1190.

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