We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.

翻译：我们研究了一个名为交互式估计的抽象交互学习框架，其目标是通过学习器查询的点与目标之间的“相似性”来估计该目标。我们引入了一种称为相异性维度的组合度量，该度量在很大程度上捕捉了模型中的可学习性。我们提出了一种简单、通用且广泛适用的算法，并对其获得了关于新维度的多项式形式的遗憾界和PAC泛化界。我们证明该框架包含并因此统一了两个经典学习模型：统计查询学习和结构化赌博机。我们还阐明了相异性维度如何与这两个框架的已知参数相关联，在某些情况下显著改进了分析结果。