Fair Best Arm Identification with Fixed Confidence
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913486810906624 |
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| author | Russo, Alessio Vannella, Filippo |
| author_facet | Russo, Alessio Vannella, Filippo |
| contents | In this work, we present a novel framework for Best Arm Identification (BAI) under fairness constraints, a setting that we refer to as \textit{F-BAI} (fair BAI). Unlike traditional BAI, which solely focuses on identifying the optimal arm with minimal sample complexity, F-BAI also includes a set of fairness constraints. These constraints impose a lower limit on the selection rate of each arm and can be either model-agnostic or model-dependent. For this setting, we establish an instance-specific sample complexity lower bound and analyze the \textit{price of fairness}, quantifying how fairness impacts sample complexity. Based on the sample complexity lower bound, we propose F-TaS, an algorithm provably matching the sample complexity lower bound, while ensuring that the fairness constraints are satisfied. Numerical results, conducted using both a synthetic model and a practical wireless scheduling application, show the efficiency of F-TaS in minimizing the sample complexity while achieving low fairness violations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fair Best Arm Identification with Fixed Confidence Russo, Alessio Vannella, Filippo Machine Learning Artificial Intelligence In this work, we present a novel framework for Best Arm Identification (BAI) under fairness constraints, a setting that we refer to as \textit{F-BAI} (fair BAI). Unlike traditional BAI, which solely focuses on identifying the optimal arm with minimal sample complexity, F-BAI also includes a set of fairness constraints. These constraints impose a lower limit on the selection rate of each arm and can be either model-agnostic or model-dependent. For this setting, we establish an instance-specific sample complexity lower bound and analyze the \textit{price of fairness}, quantifying how fairness impacts sample complexity. Based on the sample complexity lower bound, we propose F-TaS, an algorithm provably matching the sample complexity lower bound, while ensuring that the fairness constraints are satisfied. Numerical results, conducted using both a synthetic model and a practical wireless scheduling application, show the efficiency of F-TaS in minimizing the sample complexity while achieving low fairness violations. |
| title | Fair Best Arm Identification with Fixed Confidence |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2408.17313 |