Bilinear Classes: A Structural Framework for Provable Generalization in RL

Simon S. Du, Sham M. Kakade, Jason D. Lee, Shachar Lovett, Gaurav Mahajan, Wen Sun, Ruosong Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

47 Scopus citations

Abstract

This work introduces Bilinear Classes, a new structural framework, which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation. The framework incorporates nearly all existing models in which a polynomial sample complexity is achievable, and, notably, also includes new models, such as the Linear Q/V model in which both the optimal Q-function and the optimal V -function are linear in some known feature space. Our main result provides an RL algorithm which has polynomial sample complexity for Bilinear Classes; notably, this sample complexity is stated in terms of a reduction to the generalization error of an underlying supervised learning sub-problem. These bounds nearly match the best known sample complexity bounds for existing models. Furthermore, this framework also extends to the infinite dimensional (RKHS) setting: for the the Linear Q/V model, linear MDPs, and linear mixture MDPs, we provide sample complexities that have no explicit dependence on the explicit feature dimension (which could be infinite), but instead depends only on information theoretic quantities.

Original languageEnglish (US)
Title of host publicationProceedings of the 38th International Conference on Machine Learning, ICML 2021
PublisherML Research Press
Pages2826-2836
Number of pages11
ISBN (Electronic)9781713845065
StatePublished - 2021
Event38th International Conference on Machine Learning, ICML 2021 - Virtual, Online
Duration: Jul 18 2021Jul 24 2021

Publication series

NameProceedings of Machine Learning Research
Volume139
ISSN (Electronic)2640-3498

Conference

Conference38th International Conference on Machine Learning, ICML 2021
CityVirtual, Online
Period7/18/217/24/21

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

Fingerprint

Dive into the research topics of 'Bilinear Classes: A Structural Framework for Provable Generalization in RL'. Together they form a unique fingerprint.

Cite this