Integral Probability Metrics PAC-Bayes BoundsDownload PDF

Published: 31 Oct 2022, Last Modified: 12 Mar 2024NeurIPS 2022 AcceptReaders: Everyone
Keywords: PAC-Bayes, Learning Theory, Generalization bound
Abstract: We present a PAC-Bayes-style generalization bound which enables the replacement of the KL-divergence with a variety of Integral Probability Metrics (IPM). We provide instances of this bound with the IPM being the total variation metric and the Wasserstein distance. A notable feature of the obtained bounds is that they naturally interpolate between classical uniform convergence bounds in the worst case (when the prior and posterior are far away from each other), and improved bounds in favorable cases (when the posterior and prior are close). This illustrates the possibility of reinforcing classical generalization bounds with algorithm- and data-dependent components, thus making them more suitable to analyze algorithms that use a large hypothesis space.
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