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From inexact optimization to learning via gradient concentration

Author

Listed:
  • Bernhard Stankewitz

    (Humboldt University of Berlin)

  • Nicole Mücke

    (Technical University Braunschweig)

  • Lorenzo Rosasco

    (Universitá degli Studi di Genova
    CBMM, MIT & Instituto Italiano di Tecnologia)

Abstract

Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. The ultimate goal of learning, however, 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.

Suggested Citation

  • Bernhard Stankewitz & Nicole Mücke & Lorenzo Rosasco, 2023. "From inexact optimization to learning via gradient concentration," Computational Optimization and Applications, Springer, vol. 84(1), pages 265-294, January.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:1:d:10.1007_s10589-022-00408-5
    DOI: 10.1007/s10589-022-00408-5
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