On the Sample Complexity of Adversarial Multi-Source PAC Learning

TL;DR

This paper investigates the learnability of data from multiple sources when some are adversarially corrupted, showing that multi-source settings can still be PAC-learnable and offering finite-sample guarantees and benefits of cooperation.

Contribution

It demonstrates that multi-source PAC learning remains feasible despite adversarial corruption, providing new theoretical bounds and insights into collaborative learning.

Findings

Multi-source setting allows PAC-learnability despite adversarial corruption.

Finite-sample generalization bounds are established for this setting.

Sharing data in multi-source environments can be beneficial even with malicious participants.

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.