PAC-Bayes Learning Bounds for Sample-Dependent Priors

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Pranjal Awasthi, Satyen Kale, Stefani Karp, Mehryar Mohri


<p>We present a series of new PAC-Bayes learning guarantees for randomized algorithms with sample-dependent priors. Our most general bounds make no assumption on the priors and are given in terms of certain covering numbers under the infinite-Renyi divergence and the L1 distance. We show how to use these general bounds to derive leaning bounds in the setting where the sample-dependent priors obey an infinite-Renyi divergence or L1-distance sensitivity condition. We also provide a flexible framework for computing PAC-Bayes bounds, under certain stability assumptions on the sample-dependent priors, and show how to use this framework to give more refined bounds when the priors satisfy an infinite-Renyi divergence sensitivity condition.</p>