arXiv 21 Sep 2023 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2309.12162 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Zhang, Kelly and Janson, Lucas and Murphy, Susan (2020) Inference for batched bandits | 0.923 | 14 | 6 | 79% |
| 2 | Niu, Ziang and Ren, Zhimei (2025) Assumption-lean weak limits and tests for two-stage adaptive experiments | 0.874 | 5 | 2 | 100% |
| 3 | Keisuke Hirano and Jack R. Porter (2023) Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits | 0.737 | 3 | 2 | 100% |
| 4 | Hadad, Vitor and Hirshberg, David A and Zhan, Ruohan and Wager, Stef… (2021) Confidence intervals for policy evaluation in adaptive experiments | 0.644 | 2 | 2 | 100% |
| 5 | Waudby-Smith, Ian and Ramdas, Aaditya (2024) Estimating means of bounded random variables by betting | 0.585 | 3 | 1 | 100% |
| 6 | Andrews, Donald WK and Cheng, Xu and Guggenberger, Patrik (2011) Generic results for establishing the asymptotic size of confidence sets and tests | 0.511 | 2 | 2 | 50% |
| 7 | Hotz, V Joseph and Miller, Robert A (1993) Conditional choice probabilities and the estimation of dynamic models | 0.511 | 2 | 2 | 50% |
| 8 | Norets, Andriy and Takahashi, Satoru (2013) On the surjectivity of the mapping between utilities and choice probabilities | 0.511 | 2 | 2 | 50% |
| 9 | William Fithian and Dennis Sun and Jonathan Taylor (2017) Optimal Inference After Model Selection | 0.511 | 2 | 1 | 100% |
| 10 | Richard Berk and Lawrence Brown and Andreas Buja and Kai Zhang and L… (2013) Valid post-selection inference | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits | 0.644 | 2 | 2 |
| 2 | Dynamic Selection in Algorithmic Decision-making | 0.405 | 1 | 1 |
| 3 | A Primer on the Analysis of Randomized Experiments and a Survey of some Recent Advances | 0.405 | 1 | 1 |
| 4 | Valid Post-Contextual Bandit Inference | 0.405 | 1 | 1 |