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In pure-exploration problems, information is gathered sequentially to answera question on the stochastic environment. While best-arm identification forlinear bandits has been extensively studied in recent years, few works havebeen dedicated to identifying one arm that is $\varepsilon$-close to the bestone (and not exactly the best one). In this problem with several correctanswers, an identification algorithm should focus on one candidate among thoseanswers and verify that it is correct. We demonstrate that picking the answerwith highest mean does not allow an algorithm to reach asymptotic optimality interms of expected sample complexity. Instead, a \textit{furthest answer} shouldbe identified. Using that insight to choose the candidate answer carefully, wedevelop a simple procedure to adapt best-arm identification algorithms totackle $\varepsilon$-best-answer identification in transductive linearstochastic bandits. Finally, we propose an asymptotically optimal algorithm forthis setting, which is shown to achieve competitive empirical performanceagainst existing modified best-arm identification algorithms.

Choosing Answers in $\varepsilon$-Best-Answer Identification for Linear Bandits