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Continuous time asymptotic representations for adaptive experiments

Karun Adusumilli

arXiv 2 Jan 2026 · Econometrics

arXiv:2601.00739 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This article develops a continuous-time asymptotic framework for analyzing adaptive experiments -- settings in which data collection and treatment assignment evolve dynamically in response to incoming information. A key challenge in analyzing fully adaptive experiments, where the assignment policy is updated after each observation, is that the sequence of policy rules often lack a well-defined asymptotic limit. To address this, we focus instead on the empirical allocation process, which captures the fraction of observations assigned to each treatment over time. We show that, under general conditions, any adaptive experiment and its associated empirical allocation process can be approximated by a limit experiment defined by Gaussian diffusions with unknown drifts and a corresponding continuous-time allocation process. This limit representation facilitates the analysis of optimal decision rules by reducing the dimensionality of the state-space and leveraging the tractability of Gaussian diffusions. We apply the framework to derive optimal estimators, analyze in-sample regret for adaptive experiments, and construct e-processes for anytime-valid inference. Notably, we introduce the first definition of any-time and any-experiment valid inference for multi-treatment settings.

Citation extraction

26
references
46
in-text mentions
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Karun Adusumilli (2025) Risk and Optimal Policies in Bandit Experiments self1.00085100%
2Grünwald, Peter and de Heide, Rianne and Koolen, Wouter (2024) Safe Testing0.8115280%
3Adusumilli, Karun (2023) Optimal Tests Following Sequential Experiments self0.64422100%
4Hirano, Keisuke and Porter, Jack R (2023) Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits0.64422100%
5Häusler, Erich and Luschgy, Harald (2015) Stable Convergence and Stable Limit Theorems0.5113233%
6Le Cam, L (1979) A Reduction Theorem for Certain Sequential Experiments. II0.5112250%
7Ramdas, Aaditya and Grünwald, Peter and Vovk, Vladimir and Shafer, G… (2023) Game-Theoretic Statistics and Safe Anytime-Valid Inference0.51121100%
8Adusumilli, Karun (2025) How to Sample and When to Stop Sampling: The Generalised Wald Problem and Minimax Policies self0.40511100%
9Arimoto, Suguru (1972) An Algorithm for Computing the Capacity of Arbitrary Discrete Memoryless Channels0.40511100%
10Arrow, Kenneth J and Blackwell, David and Girshick, Meyer A (1949) Bayes and Minimax Solutions of Sequential Decision Problems0.40511100%

Showing the top 10 of 26 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Designing persuasive experiments0.89474