Improved Exploration in Factored Average-Reward MDPs

Mohammad Sadegh Talebi, Anders Jonsson, Odalric Maillard
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3988-3996, 2021.

Abstract

We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. Assuming a known a factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL strategy, called DBN-UCRL, which relies on Bernstein-type confidence sets defined for individual elements of the transition function. We show that for a generic factorization structure, DBN-UCRL achieves a regret bound, whose leading term strictly improves over existing regret bounds in terms of the dependencies on the size of $\cS_i$’s and the diameter. We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs. We demonstrate, through numerical experiments on standard environments, that DBN-UCRL enjoys a substantially improved regret empirically over existing algorithms that have frequentist regret guarantees.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-sadegh-talebi21a, title = { Improved Exploration in Factored Average-Reward MDPs }, author = {Sadegh Talebi, Mohammad and Jonsson, Anders and Maillard, Odalric}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3988--3996}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/talebi21a/talebi21a.pdf}, url = {https://proceedings.mlr.press/v130/sadegh-talebi21a.html}, abstract = { We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. Assuming a known a factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL strategy, called DBN-UCRL, which relies on Bernstein-type confidence sets defined for individual elements of the transition function. We show that for a generic factorization structure, DBN-UCRL achieves a regret bound, whose leading term strictly improves over existing regret bounds in terms of the dependencies on the size of $\cS_i$’s and the diameter. We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs. We demonstrate, through numerical experiments on standard environments, that DBN-UCRL enjoys a substantially improved regret empirically over existing algorithms that have frequentist regret guarantees. } }
Endnote
%0 Conference Paper %T Improved Exploration in Factored Average-Reward MDPs %A Mohammad Sadegh Talebi %A Anders Jonsson %A Odalric Maillard %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-sadegh-talebi21a %I PMLR %P 3988--3996 %U https://proceedings.mlr.press/v130/sadegh-talebi21a.html %V 130 %X We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. Assuming a known a factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL strategy, called DBN-UCRL, which relies on Bernstein-type confidence sets defined for individual elements of the transition function. We show that for a generic factorization structure, DBN-UCRL achieves a regret bound, whose leading term strictly improves over existing regret bounds in terms of the dependencies on the size of $\cS_i$’s and the diameter. We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs. We demonstrate, through numerical experiments on standard environments, that DBN-UCRL enjoys a substantially improved regret empirically over existing algorithms that have frequentist regret guarantees.
APA
Sadegh Talebi, M., Jonsson, A. & Maillard, O.. (2021). Improved Exploration in Factored Average-Reward MDPs . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3988-3996 Available from https://proceedings.mlr.press/v130/sadegh-talebi21a.html.

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