Pure Exploration with Infinite Answers

Fuente: arXiv
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Main Authors: Poiani, Riccardo, Bernasconi, Martino, Celli, Andrea
Format: Preprint
Published: 2025
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author Poiani, Riccardo
Bernasconi, Martino
Celli, Andrea
author_facet Poiani, Riccardo
Bernasconi, Martino
Celli, Andrea
contents We study pure exploration problems in which the set of correct answers is possibly infinite. For example, such problems arise when regressing a continuous function on the means of the bandit or when learning Nash equilibria by querying noisy values of the payoff matrix. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_22473
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Pure Exploration with Infinite Answers
Poiani, Riccardo
Bernasconi, Martino
Celli, Andrea
Machine Learning
We study pure exploration problems in which the set of correct answers is possibly infinite. For example, such problems arise when regressing a continuous function on the means of the bandit or when learning Nash equilibria by querying noisy values of the payoff matrix. 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.
title Pure Exploration with Infinite Answers
topic Machine Learning
url https://arxiv.org/abs/2505.22473