MDP Geometry, Normalization and Reward Balancing Solvers

Arsenii Mustafin, Aleksei Pakharev, Alex Olshevsky, Ioannis Paschalidis
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2476-2484, 2025.

Abstract

We present a new geometric interpretation of Markov Decision Processes (MDPs) with a natural normalization procedure that allows us to adjust the value function at each state without altering the advantage of any action with respect to any policy. This advantage-preserving transformation of the MDP motivates a class of algorithms which we call \emph{Reward Balancing}, which solve MDPs by iterating through these transformations, until an approximately optimal policy can be trivially found. We provide a convergence analysis of several algorithms in this class, in particular showing that for MDPs for unknown transition probabilities we can improve upon state-of-the-art sample complexity results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-mustafin25a, title = {MDP Geometry, Normalization and Reward Balancing Solvers}, author = {Mustafin, Arsenii and Pakharev, Aleksei and Olshevsky, Alex and Paschalidis, Ioannis}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2476--2484}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/mustafin25a/mustafin25a.pdf}, url = {https://proceedings.mlr.press/v258/mustafin25a.html}, abstract = {We present a new geometric interpretation of Markov Decision Processes (MDPs) with a natural normalization procedure that allows us to adjust the value function at each state without altering the advantage of any action with respect to any policy. This advantage-preserving transformation of the MDP motivates a class of algorithms which we call \emph{Reward Balancing}, which solve MDPs by iterating through these transformations, until an approximately optimal policy can be trivially found. We provide a convergence analysis of several algorithms in this class, in particular showing that for MDPs for unknown transition probabilities we can improve upon state-of-the-art sample complexity results.} }
Endnote
%0 Conference Paper %T MDP Geometry, Normalization and Reward Balancing Solvers %A Arsenii Mustafin %A Aleksei Pakharev %A Alex Olshevsky %A Ioannis Paschalidis %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-mustafin25a %I PMLR %P 2476--2484 %U https://proceedings.mlr.press/v258/mustafin25a.html %V 258 %X We present a new geometric interpretation of Markov Decision Processes (MDPs) with a natural normalization procedure that allows us to adjust the value function at each state without altering the advantage of any action with respect to any policy. This advantage-preserving transformation of the MDP motivates a class of algorithms which we call \emph{Reward Balancing}, which solve MDPs by iterating through these transformations, until an approximately optimal policy can be trivially found. We provide a convergence analysis of several algorithms in this class, in particular showing that for MDPs for unknown transition probabilities we can improve upon state-of-the-art sample complexity results.
APA
Mustafin, A., Pakharev, A., Olshevsky, A. & Paschalidis, I.. (2025). MDP Geometry, Normalization and Reward Balancing Solvers. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2476-2484 Available from https://proceedings.mlr.press/v258/mustafin25a.html.

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