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February 2014 Optimal learning with Q-aggregation
Guillaume Lecué, Philippe Rigollet
Ann. Statist. 42(1): 211-224 (February 2014). DOI: 10.1214/13-AOS1190


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.


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Guillaume Lecué. Philippe Rigollet. "Optimal learning with Q-aggregation." Ann. Statist. 42 (1) 211 - 224, February 2014.


Published: February 2014
First available in Project Euclid: 18 February 2014

zbMATH: 1286.68255
MathSciNet: MR3178462
Digital Object Identifier: 10.1214/13-AOS1190

Primary: 68Q32
Secondary: 62G05, 62G08

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 1 • February 2014
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