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A randomized online learning algorithm for better variance control

Summary: A randomized online learning algorithm for
better variance control
Jean-Yves Audibert
CERTIS - Ecole des Ponts
19, rue Alfred Nobel - Cit´e Descartes
77455 Marne-la-Vall´ee - France
Abstract. We propose a sequential randomized algorithm, which at
each step concentrates on functions having both low risk and low variance
with respect to the previous step prediction function. It satisfies a sim-
ple risk bound, which is sharp to the extent that the standard statistical
learning approach, based on supremum of empirical processes, does not
lead to algorithms with such a tight guarantee on its efficiency. Our gener-
alization error bounds complement the pioneering work of Cesa-Bianchi
et al. [12] in which standard-style statistical results were recovered with
tight constants using worst-case analysis.
A nice feature of our analysis of the randomized estimator is to put
forward the links between the probabilistic and worst-case viewpoint. It
also allows to recover recent model selection results due to Juditsky et
al. [16] and to improve them in least square regression with heavy noise,


Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure


Collections: Computer Technologies and Information Sciences