Double machine learning and design in batch adaptive experiments
We consider an experiment with at least two stages or batches and O(N)O\left(N) subjects per batch. First, we propose a semiparametric treatment effect estimator that efficiently pools information across the batches, and we show that it asymptotically dominates alternatives that aggregate single bat...
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De Gruyter
2024-11-01
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| Series: | Journal of Causal Inference |
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| Online Access: | https://doi.org/10.1515/jci-2023-0068 |
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| author | Li Harrison H. Owen Art B. |
| author_facet | Li Harrison H. Owen Art B. |
| author_sort | Li Harrison H. |
| collection | DOAJ |
| description | We consider an experiment with at least two stages or batches and O(N)O\left(N) subjects per batch. First, we propose a semiparametric treatment effect estimator that efficiently pools information across the batches, and we show that it asymptotically dominates alternatives that aggregate single batch estimates. Then, we consider the design problem of learning propensity scores for assigning treatment in the later batches of the experiment to maximize the asymptotic precision of this estimator. For two common causal estimands, we estimate this precision using observations from previous batches, and then solve a finite-dimensional concave maximization problem to adaptively learn flexible propensity scores that converge to suitably defined optima in each batch at rate Op(N−1⁄4){O}_{p}\left({N}^{-1/4}). By extending the framework of double machine learning, we show this rate suffices for our pooled estimator to attain the targeted precision after each batch, as long as nuisance function estimates converge at rate op(N−1⁄4){o}_{p}\left({N}^{-1/4}). These relatively weak rate requirements enable the investigator to avoid the common practice of discretizing the covariate space for design and estimation in batch adaptive experiments while maintaining the advantages of pooling. Our numerical study shows that such discretization often leads to substantial asymptotic and finite sample precision losses outweighing any gains from design. |
| format | Article |
| id | doaj-art-b84429a08c2b45e781021313f8f90fa5 |
| institution | Kabale University |
| issn | 2193-3685 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj-art-b84429a08c2b45e781021313f8f90fa52024-11-11T08:36:32ZengDe GruyterJournal of Causal Inference2193-36852024-11-0112155810810.1515/jci-2023-0068Double machine learning and design in batch adaptive experimentsLi Harrison H.0Owen Art B.1 Department of Statistics, Stanford University, Stanford, California, United States Department of Statistics, Stanford University, Stanford, California, United StatesWe consider an experiment with at least two stages or batches and O(N)O\left(N) subjects per batch. First, we propose a semiparametric treatment effect estimator that efficiently pools information across the batches, and we show that it asymptotically dominates alternatives that aggregate single batch estimates. Then, we consider the design problem of learning propensity scores for assigning treatment in the later batches of the experiment to maximize the asymptotic precision of this estimator. For two common causal estimands, we estimate this precision using observations from previous batches, and then solve a finite-dimensional concave maximization problem to adaptively learn flexible propensity scores that converge to suitably defined optima in each batch at rate Op(N−1⁄4){O}_{p}\left({N}^{-1/4}). By extending the framework of double machine learning, we show this rate suffices for our pooled estimator to attain the targeted precision after each batch, as long as nuisance function estimates converge at rate op(N−1⁄4){o}_{p}\left({N}^{-1/4}). These relatively weak rate requirements enable the investigator to avoid the common practice of discretizing the covariate space for design and estimation in batch adaptive experiments while maintaining the advantages of pooling. Our numerical study shows that such discretization often leads to substantial asymptotic and finite sample precision losses outweighing any gains from design.https://doi.org/10.1515/jci-2023-0068adaptive designpropensity scorepooled estimationpartially linear modelconvex optimization62k05 |
| spellingShingle | Li Harrison H. Owen Art B. Double machine learning and design in batch adaptive experiments Journal of Causal Inference adaptive design propensity score pooled estimation partially linear model convex optimization 62k05 |
| title | Double machine learning and design in batch adaptive experiments |
| title_full | Double machine learning and design in batch adaptive experiments |
| title_fullStr | Double machine learning and design in batch adaptive experiments |
| title_full_unstemmed | Double machine learning and design in batch adaptive experiments |
| title_short | Double machine learning and design in batch adaptive experiments |
| title_sort | double machine learning and design in batch adaptive experiments |
| topic | adaptive design propensity score pooled estimation partially linear model convex optimization 62k05 |
| url | https://doi.org/10.1515/jci-2023-0068 |
| work_keys_str_mv | AT liharrisonh doublemachinelearninganddesigninbatchadaptiveexperiments AT owenartb doublemachinelearninganddesigninbatchadaptiveexperiments |