Choosing Answers in $\varepsilon$-Best-Answer Identification for Linear Bandits
This addresses a gap in pure-exploration for linear bandits by focusing on ε-approximate identification, which is incremental but improves sample efficiency for applications like recommendation systems.
The paper tackles the problem of identifying an arm that is ε-close to the best one in linear bandits, showing that picking the highest mean answer is suboptimal and proposing a method based on choosing the furthest answer, which leads to an asymptotically optimal algorithm with competitive empirical performance.
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 \textit{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.