Thompson Sampling for Learning Parameterized Markov Decision Processes

Aditya Gopalan, Shie Mannor
Proceedings of The 28th Conference on Learning Theory, PMLR 40:861-898, 2015.

Abstract

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space.

Cite this Paper

BibTeX
@InProceedings{pmlr-v40-Gopalan15, title = {{Thompson Sampling for Learning Parameterized Markov Decision Processes}}, author = {Gopalan, Aditya and Mannor, Shie}, booktitle = {Proceedings of The 28th Conference on Learning Theory}, pages = {861--898}, year = {2015}, editor = {Grünwald, Peter and Hazan, Elad and Kale, Satyen}, volume = {40}, series = {Proceedings of Machine Learning Research}, address = {Paris, France}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v40/Gopalan15.pdf}, url = {https://proceedings.mlr.press/v40/Gopalan15.html}, abstract = {We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space.} }
Endnote
%0 Conference Paper %T Thompson Sampling for Learning Parameterized Markov Decision Processes %A Aditya Gopalan %A Shie Mannor %B Proceedings of The 28th Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2015 %E Peter Grünwald %E Elad Hazan %E Satyen Kale %F pmlr-v40-Gopalan15 %I PMLR %P 861--898 %U https://proceedings.mlr.press/v40/Gopalan15.html %V 40 %X We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space.
RIS
TY - CPAPER TI - Thompson Sampling for Learning Parameterized Markov Decision Processes AU - Aditya Gopalan AU - Shie Mannor BT - Proceedings of The 28th Conference on Learning Theory DA - 2015/06/26 ED - Peter Grünwald ED - Elad Hazan ED - Satyen Kale ID - pmlr-v40-Gopalan15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 40 SP - 861 EP - 898 L1 - http://proceedings.mlr.press/v40/Gopalan15.pdf UR - https://proceedings.mlr.press/v40/Gopalan15.html AB - We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space. ER -
APA
Gopalan, A. & Mannor, S.. (2015). Thompson Sampling for Learning Parameterized Markov Decision Processes. Proceedings of The 28th Conference on Learning Theory, in Proceedings of Machine Learning Research 40:861-898 Available from https://proceedings.mlr.press/v40/Gopalan15.html.

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