Fast rates of exponential cost function

Qian Sun (), Yang Zhou () and Shouyou Huang ()
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Qian Sun: Hubei Normal University
Yang Zhou: Beijing Normal University
Shouyou Huang: Hubei Normal University

Statistical Papers, 2025, vol. 66, issue 3, No 1, 19 pages

Abstract: Abstract In this paper, we introduce a new algorithm of learning with exponential cost function within the framework of statistical learning theory. We establish an important comparison theorem that illustrates the relationship between the prediction error and the excess generalization error under the moment condition. Furthermore, the paper investigates the generalization performance of algorithm and the robustness of exponential cost function. We prove that the resulting estimator enjoys asymptotic optimality and robustness under certain conditions. Numerical simulations are provided to demonstrate our theoretical findings.

Keywords: Exponential cost function; Generalization error estimation; Moment condition; Convergence rate; Covering number; 68T05; 68Q32 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01672-3

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