Estimation of subsidiary performance metrics under optimal policies
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912573575659520 |
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| author | Li, Zhaoqi Nassif, Houssam Luedtke, Alex |
| author_facet | Li, Zhaoqi Nassif, Houssam Luedtke, Alex |
| contents | In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is optimal for the primary one. The first relies on a novel margin condition that facilitates Wald-type inference. Under this and other regularity conditions, we show that the one-step corrected estimator is efficient. Despite the utility of this margin condition, it places strong restrictions on how the subsidiary metric behaves for nearly optimal policies, which may not hold in practice. We therefore introduce alternative, two-stage strategies that do not require a margin condition. The first stage constructs a set of candidate policies and the second builds a uniform confidence interval over this set. We provide numerical simulations to evaluate the performance of these methods in different scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04265 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimation of subsidiary performance metrics under optimal policies Li, Zhaoqi Nassif, Houssam Luedtke, Alex Statistics Theory In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is optimal for the primary one. The first relies on a novel margin condition that facilitates Wald-type inference. Under this and other regularity conditions, we show that the one-step corrected estimator is efficient. Despite the utility of this margin condition, it places strong restrictions on how the subsidiary metric behaves for nearly optimal policies, which may not hold in practice. We therefore introduce alternative, two-stage strategies that do not require a margin condition. The first stage constructs a set of candidate policies and the second builds a uniform confidence interval over this set. We provide numerical simulations to evaluate the performance of these methods in different scenarios. |
| title | Estimation of subsidiary performance metrics under optimal policies |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2401.04265 |