Choosing Answers in Epsilon-Best-Answer Identification for Linear Bandits

Marc Jourdan, Rémy Degenne
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:10384-10430, 2022.

Abstract

In pure-exploration problems, information is gathered sequentially to answer a question on the stochastic environment. While best-arm identification for linear bandits has been extensively studied in recent years, few works have been dedicated to identifying one arm that is $\varepsilon$-close to the best one (and not exactly the best one). In this problem with several correct answers, an identification algorithm should focus on one candidate among those answers and verify that it is correct. We demonstrate that picking the answer with highest mean does not allow an algorithm to reach asymptotic optimality in terms of expected sample complexity. Instead, a furthest answer should be identified. Using that insight to choose the candidate answer carefully, we develop a simple procedure to adapt best-arm identification algorithms to tackle $\varepsilon$-best-answer identification in transductive linear stochastic bandits. Finally, we propose an asymptotically optimal algorithm for this setting, which is shown to achieve competitive empirical performance against existing modified best-arm identification algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-jourdan22a, title = {Choosing Answers in Epsilon-Best-Answer Identification for Linear Bandits}, author = {Jourdan, Marc and Degenne, R{\'e}my}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {10384--10430}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/jourdan22a/jourdan22a.pdf}, url = {https://proceedings.mlr.press/v162/jourdan22a.html}, abstract = {In pure-exploration problems, information is gathered sequentially to answer a question on the stochastic environment. While best-arm identification for linear bandits has been extensively studied in recent years, few works have been dedicated to identifying one arm that is $\varepsilon$-close to the best one (and not exactly the best one). In this problem with several correct answers, an identification algorithm should focus on one candidate among those answers and verify that it is correct. We demonstrate that picking the answer with highest mean does not allow an algorithm to reach asymptotic optimality in terms of expected sample complexity. Instead, a furthest answer should be identified. Using that insight to choose the candidate answer carefully, we develop a simple procedure to adapt best-arm identification algorithms to tackle $\varepsilon$-best-answer identification in transductive linear stochastic bandits. Finally, we propose an asymptotically optimal algorithm for this setting, which is shown to achieve competitive empirical performance against existing modified best-arm identification algorithms.} }
Endnote
%0 Conference Paper %T Choosing Answers in Epsilon-Best-Answer Identification for Linear Bandits %A Marc Jourdan %A Rémy Degenne %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-jourdan22a %I PMLR %P 10384--10430 %U https://proceedings.mlr.press/v162/jourdan22a.html %V 162 %X In pure-exploration problems, information is gathered sequentially to answer a question on the stochastic environment. While best-arm identification for linear bandits has been extensively studied in recent years, few works have been dedicated to identifying one arm that is $\varepsilon$-close to the best one (and not exactly the best one). In this problem with several correct answers, an identification algorithm should focus on one candidate among those answers and verify that it is correct. We demonstrate that picking the answer with highest mean does not allow an algorithm to reach asymptotic optimality in terms of expected sample complexity. Instead, a furthest answer should be identified. Using that insight to choose the candidate answer carefully, we develop a simple procedure to adapt best-arm identification algorithms to tackle $\varepsilon$-best-answer identification in transductive linear stochastic bandits. Finally, we propose an asymptotically optimal algorithm for this setting, which is shown to achieve competitive empirical performance against existing modified best-arm identification algorithms.
APA
Jourdan, M. & Degenne, R.. (2022). Choosing Answers in Epsilon-Best-Answer Identification for Linear Bandits. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:10384-10430 Available from https://proceedings.mlr.press/v162/jourdan22a.html.

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