Tightening Exploration in Upper Confidence Reinforcement Learning

Hippolyte Bourel, Odalric Maillard, Mohammad Sadegh Talebi
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:1056-1066, 2020.

Abstract

The upper confidence reinforcement learning (UCRL2) algorithm introduced in \citep{jaksch2010near} is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this algorithm and its variants have remained until now mostly theoretical as numerical experiments in simple environments exhibit long burn-in phases before the learning takes place. In pursuit of practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities to compute confidence sets on the reward and (component-wise) transition distributions for each state-action pair. Furthermore, to tighten exploration, it uses an adaptive computation of the support of each transition distribution, which in turn enables us to revisit the extended value iteration procedure of UCRL2 to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments in standard environments, that reducing exploration this way yields a substantial numerical improvement compared to UCRL2 and its variants. On the theoretical side, these key modifications enable us to derive a regret bound for UCRL3 improving on UCRL2, that for the first time makes appear notions of local diameter and local effective support, thanks to variance-aware concentration bounds.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-bourel20a, title = {Tightening Exploration in Upper Confidence Reinforcement Learning}, author = {Bourel, Hippolyte and Maillard, Odalric and Talebi, Mohammad Sadegh}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {1056--1066}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/bourel20a/bourel20a.pdf}, url = {https://proceedings.mlr.press/v119/bourel20a.html}, abstract = {The upper confidence reinforcement learning (UCRL2) algorithm introduced in \citep{jaksch2010near} is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this algorithm and its variants have remained until now mostly theoretical as numerical experiments in simple environments exhibit long burn-in phases before the learning takes place. In pursuit of practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities to compute confidence sets on the reward and (component-wise) transition distributions for each state-action pair. Furthermore, to tighten exploration, it uses an adaptive computation of the support of each transition distribution, which in turn enables us to revisit the extended value iteration procedure of UCRL2 to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments in standard environments, that reducing exploration this way yields a substantial numerical improvement compared to UCRL2 and its variants. On the theoretical side, these key modifications enable us to derive a regret bound for UCRL3 improving on UCRL2, that for the first time makes appear notions of local diameter and local effective support, thanks to variance-aware concentration bounds.} }
Endnote
%0 Conference Paper %T Tightening Exploration in Upper Confidence Reinforcement Learning %A Hippolyte Bourel %A Odalric Maillard %A Mohammad Sadegh Talebi %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bourel20a %I PMLR %P 1056--1066 %U https://proceedings.mlr.press/v119/bourel20a.html %V 119 %X The upper confidence reinforcement learning (UCRL2) algorithm introduced in \citep{jaksch2010near} is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite its nice and generic theoretical regret guarantees, this algorithm and its variants have remained until now mostly theoretical as numerical experiments in simple environments exhibit long burn-in phases before the learning takes place. In pursuit of practical efficiency, we present UCRL3, following the lines of UCRL2, but with two key modifications: First, it uses state-of-the-art time-uniform concentration inequalities to compute confidence sets on the reward and (component-wise) transition distributions for each state-action pair. Furthermore, to tighten exploration, it uses an adaptive computation of the support of each transition distribution, which in turn enables us to revisit the extended value iteration procedure of UCRL2 to optimize over distributions with reduced support by disregarding low probability transitions, while still ensuring near-optimism. We demonstrate, through numerical experiments in standard environments, that reducing exploration this way yields a substantial numerical improvement compared to UCRL2 and its variants. On the theoretical side, these key modifications enable us to derive a regret bound for UCRL3 improving on UCRL2, that for the first time makes appear notions of local diameter and local effective support, thanks to variance-aware concentration bounds.
APA
Bourel, H., Maillard, O. & Talebi, M.S.. (2020). Tightening Exploration in Upper Confidence Reinforcement Learning. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:1056-1066 Available from https://proceedings.mlr.press/v119/bourel20a.html.

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