  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.
