提出不均衡样本下多任务学习的快速泛化界，突破以往只能用慢速界限制的瓶颈。
Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes
- 基于PAC-Bayesian框架，推导出不均衡样本下的可计算、可解释的快速泛化界
- 在不同任务数据量差异大的真实场景中，给出比已有边界更强的泛化保证
- 揭示不均衡设置的统计特性差异，区分两种有意义的多任务风险定义
本文针对任务训练集大小不一（即非平衡设置）的多任务与元学习场景，提出了新的快速率PAC-Bayesian泛化界。此前，此类情形仅知标准率界，而快速率界仅适用于所有训练集等大小的情况。新界具有数值可计算性和可解释性，且在多种情形下优于已有边界。除边界本身外，本文还做出概念性贡献：揭示了非平衡多任务设置与平衡情形具有不同的统计性质，证明平衡情形的证明方法无法直接推广至非平衡情形；同时阐明，在非平衡设置中存在两种合理的多任务风险定义——一种是对所有任务同等看待，另一种是给数据丰富的任务更高权重。
原文摘要 · Abstract (English)
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.
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