Online Learning as Stochastic Approximation of Regularization Paths

Details Online Learning as Stochastic Approximation of Regularization Paths Online Learning as Stochastic Approximation of Regularization Paths

2011-03-29

arxiv.org/abs/1103.5538v1

Mathematics

Probability

Scientific paper

In this paper, we analyse online learning algorithms as stochastic approximations of a regularization path converging to the regression function. We show that, through a careful adequate choice of the gain sequences, depending on regularity assumptions on the regression function, it is possible to produce the best known strong convergence rate (i.e. w.r.t. convergence in reproducing kernel Hilbert spaces) in batch learning, obtained by [Smale and Zhou 2005]. The corresponding weak convergence rate (in mean square distance) is optimal in the sense that it reaches the minimax and individual lower rate (see for instance [Caponetto and De Vito 2005]).

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