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.

翻译：我们通过吉布斯算法分析联合训练元学习算法的泛化能力。我们对元吉布斯算法期望元泛化误差的精确刻画基于对称化KL信息，该指标衡量所有元训练数据集与输出参数（包括任务特定参数和元参数）之间的依赖性。此外，我们在Steinke与Zakynthinou（2020）及Hellstrom与Durisi（2022）分别提出的超样本与超任务框架内，推导出超任务吉布斯算法元泛化误差的精确表征，该表征基于条件对称化KL信息。我们的结果还使得能够为这些适用于元学习的吉布斯算法提供新颖的无分布泛化误差上界。