Optimal Conditional Inference in Adaptive Experiments
Abstract: We study batched bandit experiments and consider the problem of inference conditional on the realized stopping time, assignment probabilities, and target parameter, where all of these may be chosen adaptively using information up to the last batch of the experiment. Absent further restrictions on the experiment, we show that inference using only the results of the last batch is optimal. When the adaptive aspects of the experiment are known to be location-invariant, in the sense that they are unchanged when we shift all batch-arm means by a constant, we show that there is additional information in the data, captured by one additional linear function of the batch-arm means. In the more restrictive case where the stopping time, assignment probabilities, and target parameter are known to depend on the data only through a collection of polyhedral events, we derive computationally tractable and optimal conditional inference procedures.
- Adusumilli, Karun, “Optimal tests following sequential experiments,” arXiv preprint arXiv:2305.00403, 2023.
- Andrews, Donald WK, Xu Cheng, and Patrik Guggenberger, “Generic results for establishing the asymptotic size of confidence sets and tests,” 2011.
- Andrews, Isaiah, Toru Kitagawa, and Adam McCloskey, “Inference on winners,” Technical Report Forthcoming.
- Berk, Richard, Lawrence Brown, Andreas Buja, Kai Zhang, and Linda Zhao, “Valid post-selection inference,” Annals of Statistics, 2013, 41 (2), 802–831.
- Fithian, William, Dennis Sun, and Jonathan Taylor, “Optimal Inference After Model Selection,” arXiv, 2017.
- Hadad, Vitor, David A Hirshberg, Ruohan Zhan, Stefan Wager, and Susan Athey, “Confidence intervals for policy evaluation in adaptive experiments,” Proceedings of the National Academy of Sciences, 2021, 118 (15), e2014602118.
- Hirano, Keisuke and Jack R. Porter, “Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits,” 2023.
- Hotz, V Joseph and Robert A Miller, “Conditional choice probabilities and the estimation of dynamic models,” The Review of Economic Studies, 1993, 60 (3), 497–529.
- Müller, Ulrich K and Andriy Norets, “Credibility of confidence sets in nonstandard econometric problems,” Econometrica, 2016, 84 (6), 2183–2213.
- Norets, Andriy and Satoru Takahashi, “On the surjectivity of the mapping between utilities and choice probabilities,” Quantitative Economics, 2013, 4 (1), 149–155.
- Rakočević, Vladimir, “On continuity of the Moore-Penrose and Drazin inverses.,” Matematichki Vesnik, 1997, 49, 163–172.
- Ramdas, Aaditya, Peter Grünwald, Vladimir Vovk, and Glenn Shafer, “Game-theoretic statistics and safe anytime-valid inference,” Statistical Science, 2023.
- Taylor, J and Y Benjamini, “RestrictedMVN: multivariate normal restricted by affine constraints,” R package version, 2016, 1.
- Zhang, Kelly, Lucas Janson, and Susan Murphy, “Inference for batched bandits,” Advances in Neural Information Processing Systems, 2020, 33, 9818–9829.
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