Bootstrap SGD: Algorithmic Stability and Robustness

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Christmann, Andreas ; Lei, Yunwen:
Bootstrap SGD: Algorithmic Stability and Robustness.
In: Analysis and Applications. Vol. 23 (2025) Issue 5 . - pp. 675-703.
ISSN 0219-5305
DOI: https://doi.org/10.1142/S0219530525400032

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In this paper, some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investigated from the view point of algorithmic stability and statistical robustness. The first two types of approaches are based on averages and are investigated from a theoretical point of view. A generalization analysis for bootstrap SGD of Type 1 and Type 2 based on algorithmic stability is done. Another type of bootstrap SGD is proposed to demonstrate that it is possible to construct purely distribution-free pointwise confidence intervals of the median curve using bootstrap SGD.