On Thompson Sampling for Smoother-than-Lipschitz Bandits

James Grant, David Leslie
; Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2612-2622, 2020.

Abstract

Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. The eluder dimension is a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling for simpler bandit problems under sub-Gaussian observation noise. We derive a new bound on the eluder dimension for classes of functions with Lipschitz derivatives, and generalise previous analyses in multiple regards.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-grant20a, title = {On Thompson Sampling for Smoother-than-Lipschitz Bandits}, author = {Grant, James and Leslie, David}, pages = {2612--2622}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, address = {Online}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/grant20a/grant20a.pdf}, url = {http://proceedings.mlr.press/v108/grant20a.html}, abstract = {Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. The eluder dimension is a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling for simpler bandit problems under sub-Gaussian observation noise. We derive a new bound on the eluder dimension for classes of functions with Lipschitz derivatives, and generalise previous analyses in multiple regards. } }
Endnote
%0 Conference Paper %T On Thompson Sampling for Smoother-than-Lipschitz Bandits %A James Grant %A David Leslie %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-grant20a %I PMLR %J Proceedings of Machine Learning Research %P 2612--2622 %U http://proceedings.mlr.press %V 108 %W PMLR %X Thompson Sampling is a well established approach to bandit and reinforcement learning problems. However its use in continuum armed bandit problems has received relatively little attention. We provide the first bounds on the regret of Thompson Sampling for continuum armed bandits under weak conditions on the function class containing the true function and sub-exponential observation noise. The eluder dimension is a recently proposed measure of the complexity of a function class, which has been demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling for simpler bandit problems under sub-Gaussian observation noise. We derive a new bound on the eluder dimension for classes of functions with Lipschitz derivatives, and generalise previous analyses in multiple regards.
APA
Grant, J. & Leslie, D.. (2020). On Thompson Sampling for Smoother-than-Lipschitz Bandits. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in PMLR 108:2612-2622

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