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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2310.19319 |
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| _version_ | 1866910969933856768 |
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| author | Qin, Chao You, Wei |
| author_facet | Qin, Chao You, Wei |
| contents | While experimental design often focuses on selecting the single best alternative from a finite set (e.g., in ranking and selection or best-arm identification), many pure-exploration problems pursue richer goals. Given a specific goal, adaptive experimentation aims to achieve it by strategically allocating sampling effort, with the underlying sample complexity characterized by a maximin optimization problem. By introducing dual variables, we derive necessary and sufficient conditions for an optimal allocation, yielding a unified algorithm design principle that extends the top-two approach beyond best-arm identification. This principle gives rise to Information-Directed Selection, a hyperparameter-free rule that dynamically evaluates and chooses among candidates based on their current informational value. We prove that, when combined with Information-Directed Selection, top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification, resolving a notable open question in the pure-exploration literature. Furthermore, our framework produces asymptotically optimal algorithms for pure-exploration thresholding bandits and $\varepsilon$-best-arm identification (i.e., ranking and selection with probability-of-good-selection guarantees), and more generally establishes a recipe for adapting Thompson sampling across a broad class of pure-exploration problems. Extensive numerical experiments highlight the efficiency of our proposed algorithms compared to existing methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_19319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dual-Directed Algorithm Design for Efficient Pure Exploration Qin, Chao You, Wei Machine Learning While experimental design often focuses on selecting the single best alternative from a finite set (e.g., in ranking and selection or best-arm identification), many pure-exploration problems pursue richer goals. Given a specific goal, adaptive experimentation aims to achieve it by strategically allocating sampling effort, with the underlying sample complexity characterized by a maximin optimization problem. By introducing dual variables, we derive necessary and sufficient conditions for an optimal allocation, yielding a unified algorithm design principle that extends the top-two approach beyond best-arm identification. This principle gives rise to Information-Directed Selection, a hyperparameter-free rule that dynamically evaluates and chooses among candidates based on their current informational value. We prove that, when combined with Information-Directed Selection, top-two Thompson sampling attains asymptotic optimality for Gaussian best-arm identification, resolving a notable open question in the pure-exploration literature. Furthermore, our framework produces asymptotically optimal algorithms for pure-exploration thresholding bandits and $\varepsilon$-best-arm identification (i.e., ranking and selection with probability-of-good-selection guarantees), and more generally establishes a recipe for adapting Thompson sampling across a broad class of pure-exploration problems. Extensive numerical experiments highlight the efficiency of our proposed algorithms compared to existing methods. |
| title | Dual-Directed Algorithm Design for Efficient Pure Exploration |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2310.19319 |