Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes

TL;DR

This paper introduces new fast-rate PAC-Bayesian generalization bounds for multi-task and meta-learning with unbalanced task sample sizes, providing stronger guarantees and insights into the statistical properties of such settings.

Contribution

The paper develops the first fast-rate bounds for unbalanced multi-task learning and analyzes the different statistical properties compared to balanced scenarios.

Findings

Bounds are numerically computable and interpretable.

Unbalanced setting exhibits different statistical properties than balanced.

Provides two meaningful definitions of multi-task risk based on task importance.

Abstract

We present new fast-rate PAC-Bayesian generalization bounds for multi-task and meta-learning in the unbalanced setting, i.e. when the tasks have training sets of different sizes, as is typically the case in real-world scenarios. Previously, only standard-rate bounds were known for this situation, while fast-rate bounds were limited to the setting where all training sets are of equal size. Our new bounds are numerically computable as well as interpretable, and we demonstrate their flexibility in handling a number of cases where they give stronger guarantees than previous bounds. Besides the bounds themselves, we also make conceptual contributions: we demonstrate that the unbalanced multi-task setting has different statistical properties than the balanced situation, specifically that proofs from the balanced situation do not carry over to the unbalanced setting. Additionally, we shed light on the fact that the unbalanced situation allows two meaningful definitions of multi-task risk, depending on whether all tasks should be considered equally important or if sample-rich tasks should receive more weight than sample-poor ones.