$ $The classical theory of statistical estimation aims to estimate a
parameter of interest under data generated from a fixed design ("offline
estimation"), while the contemporary theory of online learning provides
algorithms for estimation under adaptively chosen covariates ("online
estimation"). Motivated by connections between estimation and interactive
decision making, we ask: is it possible to convert offline estimation
algorithms into online estimation algorithms in a black-box fashion? We
investigate this question from an information-theoretic perspective by
introducing a new framework, Oracle-Efficient Online Estimation (OEOE), where
the learner can only interact with the data stream indirectly through a
sequence of offline estimators produced by a black-box algorithm operating on
the stream. Our main results settle the statistical and computational
complexity of online estimation in this framework.
$\bullet$ Statistical complexity. We show that information-theoretically,
there exist algorithms that achieve near-optimal online estimation error via
black-box offline estimation oracles, and give a nearly-tight characterization
for minimax rates in the OEOE framework.
$\bullet$ Computational complexity. We show that the guarantees above cannot
be achieved in a computationally efficient fashion in general, but give a
refined characterization for the special case of conditional density
estimation: computationally efficient online estimation via black-box offline
estimation is possible whenever it is possible via unrestricted algorithms.
Finally, we apply our results to give offline oracle-efficient algorithms for
interactive decision making.

统计估计的经典理论和在线学习的现代理论相结合，提出了黑盒离线估计到在线估计的转化问题，通过引入 Oracle-Efficient Online Estimation (OEOE) 框架，从信息论的角度解决了在线估计的统计复杂性和计算复杂性，并将结果应用于交互决策制定。

在线估计通过离线估计：一种信息论框架

Online Estimation via Offline Estimation: An Information-Theoretic  Framework

To perform inference after model selection, we propose controlling the
selective type I error; i.e., the error rate of a test given that it was
performed. By doing so, we recover long-run frequency properties among selected
hypotheses analogous to those that apply in the classical (non-adaptive)
context. Our proposal is closely related to data splitting and has a similar
intuitive justification, but is more powerful. Exploiting the classical theory
of Lehmann and Scheff\'e (1955), we derive most powerful unbiased selective
tests and confidence intervals for inference in exponential family models after
arbitrary selection procedures. For linear regression, we derive new selective
z-tests that generalize recent proposals for inference after model selection
and improve on their power, and new selective t-tests that do not require
knowledge of the error variance.

该研究提出一种控制选择性 I 型错误的方法，以恢复经典情境下适用的选定假设的长期频率性质，推导出一些用于指数家族模型的最强无偏选择性检验和置信区间以及线性回归模型的新型选择性 z 和 t 检验。