Pure Exploration with Infinite Answers

ArXi:2505.22473v2 Announce Type: replace 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 general setting.