Simultaneous Model Selection and Optimization through Parameter-free Stochastic Learning

TL;DR

This paper introduces a parameter-free kernel-based stochastic gradient descent algorithm that simultaneously performs model selection and training without cross-validation, achieving optimal convergence rates.

Contribution

It presents a novel online learning algorithm that estimates regularization parameters dynamically during training, eliminating the need for parameter tuning or validation.

Findings

Algorithm performs model selection during training.

Achieves optimal convergence rates under standard assumptions.

No parameters to tune or cross-validation needed.

Abstract

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection phase is often ignored. In fact, in theoretical works most of the time assumptions are made, for example, on the prior knowledge of the norm of the optimal solution, while in the practical world validation methods remain the only viable approach. In this paper, we propose a new kernel-based stochastic gradient descent algorithm that performs model selection while training, with no parameters to tune, nor any form of cross-validation. The algorithm builds on recent advancement in online learning theory for unconstrained settings, to estimate over time the right regularization in a data-dependent way. Optimal rates of convergence are proved under standard smoothness assumptions on the target function, using the range space of the fractional integral operator associated with the kernel.