Gamification of Pure Exploration for Linear Bandits

Rémy Degenne, Pierre Menard, Xuedong Shang, Michal Valko
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2432-2442, 2020.

Abstract

We investigate an active \emph{pure-exploration} setting, that includes \emph{best-arm identification}, in the context of \emph{linear stochastic bandits}. While asymptotically optimal algorithms exist for standard \emph{multi-armed bandits}, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-degenne20a, title = {Gamification of Pure Exploration for Linear Bandits}, author = {Degenne, R{\'e}my and Menard, Pierre and Shang, Xuedong and Valko, Michal}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2432--2442}, 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/degenne20a/degenne20a.pdf}, url = {http://proceedings.mlr.press/v119/degenne20a.html}, abstract = {We investigate an active \emph{pure-exploration} setting, that includes \emph{best-arm identification}, in the context of \emph{linear stochastic bandits}. While asymptotically optimal algorithms exist for standard \emph{multi-armed bandits}, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.} }
Endnote
%0 Conference Paper %T Gamification of Pure Exploration for Linear Bandits %A Rémy Degenne %A Pierre Menard %A Xuedong Shang %A Michal Valko %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-degenne20a %I PMLR %P 2432--2442 %U http://proceedings.mlr.press/v119/degenne20a.html %V 119 %X We investigate an active \emph{pure-exploration} setting, that includes \emph{best-arm identification}, in the context of \emph{linear stochastic bandits}. While asymptotically optimal algorithms exist for standard \emph{multi-armed bandits}, the existence of such algorithms for the best-arm identification in linear bandits has been elusive despite several attempts to address it. First, we provide a thorough comparison and new insight over different notions of optimality in the linear case, including G-optimality, transductive optimality from optimal experimental design and asymptotic optimality. Second, we design the first asymptotically optimal algorithm for fixed-confidence pure exploration in linear bandits. As a consequence, our algorithm naturally bypasses the pitfall caused by a simple but difficult instance, that most prior algorithms had to be engineered to deal with explicitly. Finally, we avoid the need to fully solve an optimal design problem by providing an approach that entails an efficient implementation.
APA
Degenne, R., Menard, P., Shang, X. & Valko, M.. (2020). Gamification of Pure Exploration for Linear Bandits. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2432-2442 Available from http://proceedings.mlr.press/v119/degenne20a.html.

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