A fundamental challenge in interactive learning and decision making, ranging from bandit problems to reinforcement learning, is to provide sample-efficient, adaptive learning algorithms that achieve near-optimal regret. This question is analogous to the classical problem of optimal (supervised) statistical learning, where there are well-known complexity measures (e.g., VC dimension and Rademacher complexity) that govern the statistical complexity of learning. However, characterizing the statistical complexity of interactive learning is substantially more challenging due to the adaptive nature of the problem. The main result of this work provides a complexity measure, the Decision-Estimation Coefficient, that is proven to be both necessary and sufficient for sample-efficient interactive learning. In particular, we provide: 1. a lower bound on the optimal regret for any interactive decision making problem, establishing the Decision-Estimation Coefficient as a fundamental limit. 2. a unified algorithm design principle, Estimation-to-Decisions (E2D), which transforms any algorithm for supervised estimation into an online algorithm for decision making. E2D attains a regret bound matching our lower bound, thereby achieving optimal sample-efficient learning as characterized by the Decision-Estimation Coefficient. Taken together, these results constitute a theory of learnability for interactive decision making. When applied to reinforcement learning settings, the Decision-Estimation Coefficient recovers essentially all existing hardness results and lower bounds. More broadly, the approach can be viewed as a decision-theoretic analogue of the classical Le Cam theory of statistical estimation; it also unifies a number of existing approaches -- both Bayesian and frequentist.

提供决策-评估系数，作为评估交互式学习复杂度的量，从而实现与样本效率无关的最佳后悔，同时引入了一种新的选择Estimation-to-Decisions（E2D），使得监督学习的算法适应于在线决策，从而实现了准确的与样本效率无关的学习，在强化学习中，该决策-评估系数可以快速恢复现有的大多数困难结果和下限。

交互式决策的统计复杂度