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- W2950291451 abstract "We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for SGD which depend on the worst-case constants. By virtue of the data-dependent argument, our bounds provide new insights into learning with SGD on convex and non-convex problems. In the convex case, we show that the bound on the generalization error depends on the risk at the initialization point. In the non-convex case, we prove that the expected curvature of the objective function around the initialization point has crucial influence on the generalization error. In both cases, our results suggest a simple data-driven strategy to stabilize SGD by pre-screening its initialization. As a corollary, our results allow us to show optimistic generalization bounds that exhibit fast convergence rates for SGD subject to a vanishing empirical risk and low noise of stochastic gradient." @default.
- W2950291451 created "2019-06-27" @default.
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- W2950291451 creator A5068085751 @default.
- W2950291451 date "2017-03-05" @default.
- W2950291451 modified "2023-09-24" @default.
- W2950291451 title "Data-Dependent Stability of Stochastic Gradient Descent" @default.
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