We analyze the generalization ability of joint-training meta learning algorithms via the Gibbs algorithm. Our exact characterization of the expected meta generalization error for the meta Gibbs algorithm is based on symmetrized KL information, which measures the dependence between all meta-training datasets and the output parameters, including task-specific and meta parameters. Additionally, we derive an exact characterization of the meta generalization error for the super-task Gibbs algorithm, in terms of conditional symmetrized KL information within the super-sample and super-task framework introduced in Steinke and Zakynthinou (2020) and Hellstrom and Durisi (2022) respectively. Our results also enable us to provide novel distribution-free generalization error upper bounds for these Gibbs algorithms applicable to meta learning.

通过 Gibbs 算法分析联合训练元学习算法的泛化能力，其中对元 Gibbs 算法的预期元泛化误差进行了精确刻画，基于对称 KL 信息度量所有元训练数据集和输出参数（包括特定任务和元参数）之间的依赖性。此外，我们还推导出了超任务 Gibbs 算法的元泛化误差的精确刻画，以超样本和超任务框架为基础。我们的结果还使我们能够为这些 Gibbs 算法提供新的分布自由泛化误差上界，适用于元学习。

关于用于 Gibbs 算法的元学习的泛化误差