This work investigates the offline formulation of the contextual bandit problem, where the goal is to leverage past interactions collected under a behavior policy to evaluate, select, and learn new, potentially better-performing, policies. Motivated by critical applications, we move beyond point estimators. Instead, we adopt the principle of pessimism where we construct upper bounds that assess a policy's worst-case performance, enabling us to confidently select and learn improved policies. Precisely, we introduce novel, fully empirical concentration bounds for a broad class of importance weighting risk estimators. These bounds are general enough to cover most existing estimators and pave the way for the development of new ones. In particular, our pursuit of the tightest bound within this class motivates a novel estimator (LS), that logarithmically smooths large importance weights. The bound for LS is provably tighter than its competitors, and naturally results in improved policy selection and learning strategies. Extensive policy evaluation, selection, and learning experiments highlight the versatility and favorable performance of LS.

翻译：本研究探讨上下文赌博机问题的离线形式，其目标在于利用行为策略收集的历史交互数据来评估、选择和学习新的、可能具有更优性能的策略。受关键应用场景驱动，我们超越了点估计方法，转而采用悲观主义原则：通过构建评估策略最坏情况性能的上界，使我们能够可靠地选择和学习改进后的策略。具体而言，我们针对广泛的重要性加权风险估计器类别，提出了全新的完全经验集中界。这些界限具有足够的普适性，能够涵盖大多数现有估计器，并为开发新型估计器开辟道路。特别地，为追求该类估计器中最紧致的边界，我们提出了一种新型估计器（LS），通过对较大重要性权重进行对数平滑处理。理论证明LS的边界较现有方法更为紧致，并自然衍生出改进的策略选择与学习策略。大量策略评估、选择与学习实验验证了LS方法的通用性及其优越性能。