The Value Function Polytope in Reinforcement Learning. Dadashi, R.; Taïga, A. A.; Roux, N. L.; Schuurmans, D.; and Bellemare, M. G.
The Value Function Polytope in Reinforcement Learning [link]Paper  abstract   bibtex   
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.
@article{dadashiValueFunctionPolytope2019,
  archivePrefix = {arXiv},
  eprinttype = {arxiv},
  eprint = {1901.11524},
  primaryClass = {cs, stat},
  title = {The {{Value Function Polytope}} in {{Reinforcement Learning}}},
  url = {http://arxiv.org/abs/1901.11524},
  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.},
  urldate = {2019-02-05},
  date = {2019-01-31},
  keywords = {Statistics - Machine Learning,Computer Science - Artificial Intelligence,Computer Science - Machine Learning},
  author = {Dadashi, Robert and Taïga, Adrien Ali and Roux, Nicolas Le and Schuurmans, Dale and Bellemare, Marc G.},
  file = {/home/dimitri/Nextcloud/Zotero/storage/BMAG529V/Dadashi et al. - 2019 - The Value Function Polytope in Reinforcement Learn.pdf;/home/dimitri/Nextcloud/Zotero/storage/NKH528QV/1901.html}
}
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