Fast rate bounds for multi-task and meta-learning with different sample sizes

conference paper Fast rate bounds for multi-task and meta-learning with different sample sizes Advances in Neural Information Processing Systems published yes Hossein Zakerinia author 653bd8b6-f394-11eb-9cf6-c0bbf6cd78d40009-0007-3977-6462 Christoph Lampert author 40C20FD2-F248-11E8-B48F-1D18A9856A870000-0001-8622-7887 GradSch department ChLa department NeurIPS: Neural Information Processing Systems 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 samplepoor ones. Neural Information Processing Systems Foundation2025San Diego, CA, United States eng 39th Conference on Neural Information Processing Systems 1049-5258 979833133827510.52202/085713-0278 389062-9093 Zakerinia, Hossein, and Christoph Lampert. “Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes.” In 39th Conference on Neural Information Processing Systems, 38:9062–93. Neural Information Processing Systems Foundation, 2025. <a href="https://doi.org/10.52202/085713-0278">https://doi.org/10.52202/085713-0278</a>. H. Zakerinia, C. Lampert, in:, 39th Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2025, pp. 9062–9093. Zakerinia, H., & Lampert, C. (2025). Fast rate bounds for multi-task and meta-learning with different sample sizes. In 39th Conference on Neural Information Processing Systems (Vol. 38, pp. 9062–9093). San Diego, CA, United States: Neural Information Processing Systems Foundation. <a href="https://doi.org/10.52202/085713-0278">https://doi.org/10.52202/085713-0278</a> H. Zakerinia and C. Lampert, “Fast rate bounds for multi-task and meta-learning with different sample sizes,” in 39th Conference on Neural Information Processing Systems, San Diego, CA, United States, 2025, vol. 38, pp. 9062–9093. Zakerinia H, Lampert C. Fast rate bounds for multi-task and meta-learning with different sample sizes. In: 39th Conference on Neural Information Processing Systems. Vol 38. Neural Information Processing Systems Foundation; 2025:9062-9093. doi:<a href="https://doi.org/10.52202/085713-0278">10.52202/085713-0278</a> Zakerinia, Hossein, and Christoph Lampert. “Fast Rate Bounds for Multi-Task and Meta-Learning with Different Sample Sizes.” 39th Conference on Neural Information Processing Systems, vol. 38, Neural Information Processing Systems Foundation, 2025, pp. 9062–93, doi:<a href="https://doi.org/10.52202/085713-0278">10.52202/085713-0278</a>. Zakerinia H, Lampert C. 2025. Fast rate bounds for multi-task and meta-learning with different sample sizes. 39th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 38, 9062–9093. 228242026-09-06T22:01:59Z2026-09-10T08:37:33Z