The Value Function Polytope in Reinforcement Learning
Machine Learning
2019-05-17 v3 Artificial Intelligence
Machine Learning
Abstract
We establish geometric and topological properties of the space of value functions in finite state-action Markov decision processes. Our main contribution is the characterization of the nature of its shape: a general polytope (Aigner et al., 2010). To demonstrate this result, we exhibit several properties of the structural relationship between policies and value functions including the line theorem, which shows that the value functions of policies constrained on all but one state describe a line segment. Finally, we use this novel perspective to introduce visualizations to enhance the understanding of the dynamics of reinforcement learning algorithms.
Cite
@article{arxiv.1901.11524,
title = {The Value Function Polytope in Reinforcement Learning},
author = {Robert Dadashi and Adrien Ali Taïga and Nicolas Le Roux and Dale Schuurmans and Marc G. Bellemare},
journal= {arXiv preprint arXiv:1901.11524},
year = {2019}
}