PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

Code

• github.com/jonasrothfuss/meta_learning_pacoh
  OfficialIn paperpytorch★ 26
• github.com/jonasrothfuss/pacoh_nn
  tf★ 3
• github.com/yilun-wu/MetaL-Benchmark
  none★ 0

Abstract

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.

Tasks

Reproductions