An Information-Theoretic Analysis of Out-of-Distribution Generalization in Meta-Learning with Applications to Meta-RL
Xingtu Liu
TL;DR
This work develops an information-theoretic framework for out-of-distribution generalization in meta-learning and meta-reinforcement learning. It derives mutual-information and conditional mutual-information bounds that quantify how environment shifts and task-specific adaptation affect OOD generalization, covering both standard distribution-mismatch and broad-to-narrow subtask settings. For meta-RL, the authors extend these bounds to the RL objective and analyze a gradient-based meta-RL algorithm with noisy updates, linking generalization error to suboptimality in target environments and in offline RL via Bellman-error estimators. The results illuminate how environment mismatch, task uncertainty, and adaptation dynamics constrain reliable transfer, offering guidance for designing meta-learning and meta-RL methods with robust OOD performance.
Abstract
In this work, we study out-of-distribution generalization in meta-learning from an information-theoretic perspective. We focus on two scenarios: (i) when the testing environment mismatches the training environment, and (ii) when the training environment is broader than the testing environment. The first corresponds to the standard distribution mismatch setting, while the second reflects a broad-to-narrow training scenario. We further formalize the generalization problem in meta-reinforcement learning and establish corresponding generalization bounds. Finally, we analyze the generalization performance of a gradient-based meta-reinforcement learning algorithm.