On the Sample Complexity of Adversarial Multi-Source PAC Learning

Abstract

We study the problem of learning from multiple untrusted data sources, a scenario of increasing practical relevance given the recent emergence of crowdsourcing and collaborative learning paradigms. Specifically, we analyze the situation in which a learning system obtains datasets from multiple sources, some of which might be biased or even adversarially perturbed. It is known that in the single-source case, an adversary with the power to corrupt a fixed fraction of the training data can prevent PAC-learnability, that is, even in the limit of infinitely much training data, no learning system can approach the optimal test error. In this work we show that, surprisingly, the same is not true in the multi-source setting, where the adversary can arbitrarily corrupt a fixed fraction of the data sources. Our main results are a generalization bound that provides finite-sample guarantees for this learning setting, as well as corresponding lower bounds. Besides establishing PAC-learnability our results also show that in a cooperative learning setting sharing data with other parties has provable benefits, even if some participants are malicious.

A No-Free-Lunch Theorem for MultiTask Learning

“…For the multisource case N 1, to the best of our knowledge, situations of negative transfer have only been described in adversarial settings with corrupted labels. For instance, the recent papers of [Qia18,MMM19,KFAL20] show limits of multitask under various adversarial corruption of labels in datasets, while [SZ19] derives a positive result, i.e., rates (for Lipschitz loss) decreasing in both N and n, up to excluded or downweighted datasets. The procedure of [SZ19] is however nonadaptive as it requires known noise proportions.…”