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Algorithmic Stability and Hypothesis Complexity
Tongliang Liu · Gábor Lugosi · Gergely Neu · Dacheng Tao

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #97

We introduce a notion of algorithmic stability of learning algorithms---that we term \emph{hypothesis stability}---that captures stability of the hypothesis output by the learning algorithm in the normed space of functions from which hypotheses are selected. The main result of the paper bounds the generalization error of any learning algorithm in terms of its hypothesis stability. The bounds are based on martingale inequalities in the Banach space to which the hypotheses belong. We apply the general bounds to bound the performance of some learning algorithms based on empirical risk minimization and stochastic gradient descent.

Author Information

Tongliang Liu (The University of Sydney)
Gábor Lugosi (Universitat Pompeu Fabra)
Gergely Neu (Universitat Pompeu Fabra / Google Brain Zürich)
Dacheng Tao

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