Non-parametric Stochastic Approximation with Large Step sizes

Aymeric Dieuleveut; Francis Bach

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arXiv · 1408.0361

Non-parametric Stochastic Approximation with Large Step sizes

Aymeric Dieuleveut·Francis Bach

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Abstract

We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS $\mathcal{H}$, even if the optimal predictor (i.e., the conditional expectation) is not in $\mathcal{H}$. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized least-mean-square algorithm (a form of stochastic gradient), given a sufficient large step-size, attains optimal rates of convergence for a variety of regimes for the smoothnesses of the optimal prediction function and the functions in $\mathcal{H}$.

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Aymeric Dieuleveut, Francis Bach. 2014-08-02. Non-parametric Stochastic Approximation with Large Step sizes. https://arxiv.org/abs/1408.0361

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