Bootstrap SGD: Algorithmic Stability and Robustness
This work addresses statistical robustness in optimization for machine learning, but it appears incremental as it builds on existing bootstrap and SGD techniques.
The paper tackles the problem of using empirical bootstrap methods with stochastic gradient descent (SGD) to minimize empirical risk, focusing on algorithmic stability and robustness, and proposes a method for constructing distribution-free confidence intervals for the median curve.
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.