Bootstrap SGD: Algorithmic Stability and Robustness

TL;DR

This paper explores bootstrap methods for stochastic gradient descent (SGD) to enhance stability and robustness, providing theoretical analysis and a new approach for distribution-free confidence intervals in empirical risk minimization.

Contribution

It introduces novel bootstrap SGD algorithms with theoretical stability analysis and demonstrates their ability to produce distribution-free confidence intervals.

Findings

Theoretical generalization bounds for bootstrap SGD methods.

Proposed bootstrap SGD approach for distribution-free median curve confidence intervals.

Empirical validation of stability and robustness improvements.

Abstract

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.