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

2025-05-21

AI Summary

This work addresses the challenging problem of generalization analysis in multi-task learning and meta-learning under task-level sample-size heterogeneity—i.e., imbalanced training set sizes across tasks. We establish, for the first time, computable and tight fast-rate generalization bounds tailored to this setting. Unlike prior fast-rate results restricted to equal-sample-size assumptions, our analysis leverages empirical process theory, Rademacher complexity, and task-weighted modeling to characterize the distinct bias–variance trade-off induced by heterogeneity. Specifically, we formally define two natural multi-task risks: task-equal-weighted risk and sample-weighted risk, and reveal their fundamental divergence in generalization behavior. Empirical evaluation demonstrates that our bounds significantly outperform classical standard-rate bounds across diverse practical configurations, providing both theoretical foundations and a practical diagnostic tool for imbalanced multi-task learning.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Multiagent Systems: Multiagent Learning
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We present new fast-rate 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 if all tasks should be considered equally important or if sample-rich tasks should receive more weight than sample-poor ones.

Problem

• Generalization bounds for unbalanced multi-task learning
• Comparing statistical properties of balanced vs unbalanced settings
• Defining multi-task risk for sample-rich vs sample-poor tasks

Innovation

• Fast-rate bounds for unbalanced multi-task learning
• Numerically computable and interpretable generalization bounds
• Two meaningful definitions of multi-task risk