Pure Exploration with Infinite Answers

Riccardo Poiani, Martino Bernasconi, Andrea Celli

TL;DR: We develop tight lower bounds and algorithms for pure exploration problems where the set of correct answers for each bandit is possibly infinite.

Abstract: We study pure exploration problems where the set of correct answers is possibly infinite, e.g., the regression of any continuous function of the means of the bandit. We derive an instance-dependent lower bound for these problems. By analyzing it, we discuss why existing methods (i.e., Sticky Track-and-Stop) for finite answer problems fail at being asymptotically optimal in this more general setting. Finally, we present a framework, Sticky-Sequence Track-and-Stop, which generalizes both Track-and-Stop and Sticky Track-and-Stop, and that enjoys asymptotic optimality. Due to its generality, our analysis also highlights special cases where existing methods enjoy optimality.

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Code Dataset Url: https://github.com/riccardopoiani/infinite-answers

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Submission Number: 1341