Empirical Bayes for compound adaptive experiments

Abstract

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.

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BibTeX RIS

BibTeX

@misc{adusumilli2026empirical,
  title = {{Empirical Bayes for compound adaptive experiments}},
  author = {Karun Adusumilli and Jiaying Gu and Junfan Tao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17158},
  eprint = {2609.17158},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17158},
}

RIS

TY  - UNPB
TI  - Empirical Bayes for compound adaptive experiments
AU  - Karun Adusumilli
AU  - Jiaying Gu
AU  - Junfan Tao
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.17158
UR  - https://arxiv.org/abs/2609.17158
AB  - 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.
ER  -

Abstract

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