OPTIMAL LEARNING WITH Q-AGGREGATION

• 成果类型: Article
• 署名作者: Lecue, Guillaume; Rigollet, Philippe
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1190
• 发表日期: 2014
• 页码: 211-224
• 关键词: empirical risk minimization; pac-bayesian bounds; Optimal Rates; CLASSIFICATION

摘要

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.