Meta-Frieren: Beyond Single Level Online Learning

Vahan Arsenyan, Arnak Dalalyan

We study a two-stage online optimization problem: at each round, a meta-learner first selects an agent-environment pair, then the chosen agent interacts with the environment, and receives a reward. We introduce Meta-Frieren, a general framework for maximizing cumulative reward in this setting. Our analysis yields a simple UCB-style criterion for meta-level selection and recovers prior guarantees as special cases while extending them to broader settings. We instantiate Meta-Frieren with GP-UCB under Bayesian and frequentist assumptions. We also derive, to our knowledge, the first high-probability regret bound for Feel-Good Thompson Sampling, specialize it to finite and parametric function classes, and integrate it into Meta-Frieren. Experiments support our theoretical results and demonstrate that Meta-Frieren can be successfully applied to hyperparameter optimization across multiple model classes.