The Adaptive Doubly Robust Estimator and a Paradox Concerning Logging Policy

Abstract

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples without non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.

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Cite

Text

Kato et al. "The Adaptive Doubly Robust Estimator and a Paradox Concerning Logging Policy." Neural Information Processing Systems, 2021.

Markdown

[Kato et al. "The Adaptive Doubly Robust Estimator and a Paradox Concerning Logging Policy." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/kato2021neurips-adaptive/)

BibTeX

@inproceedings{kato2021neurips-adaptive,
  title     = {{The Adaptive Doubly Robust Estimator and a Paradox Concerning Logging Policy}},
  author    = {Kato, Masahiro and McAlinn, Kenichiro and Yasui, Shota},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/kato2021neurips-adaptive/}
}