复合自适应实验的经验贝叶斯方法

中文摘要 AI 辅助

我们研究了复合自适应实验背景下的经验贝叶斯（EB）方法，其中每个实验中的臂分布遵循正态分布，其均值未知，我们旨在估计该均值。存在两种主要的EB策略：$g$-建模，通过最大化边际似然来估计先验；以及$f$-建模，直接从观测值的经验分布推导后验均值。我们证明，即使$g$-建模错误地假设数据是外生收集的，它仍然是一种有效的EB程序；其有效性不依赖于特定的采样算法，也不依赖于样本量是否内生。在实践中，可以假装数据是外生采样的，从而应用标准的$g$-建模技术。我们将遗憾保证从外生采样扩展到自适应生成的数据。相比之下，如标准$f$-建模那样，基于观测数据的边际密度天真地应用Tweedie公式，在自适应采样下可能产生有偏的规则。我们通过使用广泛采用的自适应算法的模拟实验证实了$g$-建模的稳健性，并使用包含多个序贯实验的真实数据集展示了其适用性。

英文摘要

We investigate Empirical Bayes (EB) methods in the context of compound adaptive experiments, where the arm distribution in each experiment follows a normal distribution with an unknown mean that we seek to estimate. There are two main EB strategies: $g$-modeling, which estimates the prior by maximizing the marginal likelihood, and $f$-modeling, which derives posterior means directly from the empirical distribution of the observations. We show that $g$-modeling continues to be a valid EB procedure even when it incorrectly assumes that data are collected exogenously; its validity does not depend on the particular sampling algorithm or on whether sample sizes are endogenous. In practice, one can apply standard $g$-modeling techniques by acting as though the data were exogenously sampled. We extend regret guarantees from exogenous sampling to adaptively generated data. By contrast, naively applying the Tweedie formula based on the marginal density of the observed data, as in standard $f$-modeling, can produce biased rules under adaptive sampling. We corroborate the robustness of $g$-modeling through simulations with widely used adaptive algorithms and demonstrate its applicability using a real-world dataset consisting of multiple sequential experiments.

发表机构

• University of Pennsylvania（宾夕法尼亚大学）
• University of Toronto（多伦多大学）
• Kyoto University（京都大学）

机构由 AI 辅助整理，请以论文原文为准。