Minimax statistical learning with Wasserstein distances

Jaeho Lee, Maxim Raginsky

Research output: Contribution to journalConference articlepeer-review


As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this work, we describe a minimax framework for statistical learning with ambiguity sets given by balls in Wasserstein space. In particular, we prove generalization bounds that involve the covering number properties of the original ERM problem. As an illustrative example, we provide generalization guarantees for transport-based domain adaptation problems where the Wasserstein distance between the source and target domain distributions can be reliably estimated from unlabeled samples.

Original languageEnglish (US)
Pages (from-to)2687-2696
Number of pages10
JournalAdvances in Neural Information Processing Systems
StatePublished - 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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