From inexact optimization to learning via gradient concentration

Bernhard Stankewitz; Nicole Mücke; Lorenzo Rosasco

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arXiv · 2106.05397

From inexact optimization to learning via gradient concentration

Bernhard Stankewitz·Nicole Mücke·Lorenzo Rosasco

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Abstract

Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training data provides only partial information. In this view, the optimization problems that are practically feasible are based on inexact quantities that are stochastic in nature. In this paper, we show how probabilistic results, specifically gradient concentration, can be combined with results from inexact optimization to derive sharp test error guarantees. By considering unconstrained objectives we highlight the implicit regularization properties of optimization for learning.

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Bernhard Stankewitz, Nicole Mücke, Lorenzo Rosasco. 2021-06-09. From inexact optimization to learning via gradient concentration. https://arxiv.org/abs/2106.05397

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