English

Coarse-Grained Smoothness for RL in Metric Spaces

Machine Learning 2021-10-26 v1

Abstract

Principled decision-making in continuous state--action spaces is impossible without some assumptions. A common approach is to assume Lipschitz continuity of the Q-function. We show that, unfortunately, this property fails to hold in many typical domains. We propose a new coarse-grained smoothness definition that generalizes the notion of Lipschitz continuity, is more widely applicable, and allows us to compute significantly tighter bounds on Q-functions, leading to improved learning. We provide a theoretical analysis of our new smoothness definition, and discuss its implications and impact on control and exploration in continuous domains.

Keywords

Cite

@article{arxiv.2110.12276,
  title  = {Coarse-Grained Smoothness for RL in Metric Spaces},
  author = {Omer Gottesman and Kavosh Asadi and Cameron Allen and Sam Lobel and George Konidaris and Michael Littman},
  journal= {arXiv preprint arXiv:2110.12276},
  year   = {2021}
}
R2 v1 2026-06-24T07:07:46.701Z