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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2504.17019 |
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| _version_ | 1866909591190634496 |
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| author | Al-Thani, Hessa Nagarajan, Viswanath |
| author_facet | Al-Thani, Hessa Nagarajan, Viswanath |
| contents | We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $δ$, the goal is to find a value that is $δ$-approximately minimum (or maximum) over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a $δ$-minimum value or a $δ$-minimizer. When all query costs are uniform, we provide a $4$-approximation algorithm for both variants. When query costs are non-uniform, we provide a $5.83$-approximation algorithm for the $δ$-minimum value and a $7.47$-approximation for the $δ$-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding ''adaptivity'' gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying Approximate Minimizers under Stochastic Uncertainty Al-Thani, Hessa Nagarajan, Viswanath Data Structures and Algorithms We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $δ$, the goal is to find a value that is $δ$-approximately minimum (or maximum) over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a $δ$-minimum value or a $δ$-minimizer. When all query costs are uniform, we provide a $4$-approximation algorithm for both variants. When query costs are non-uniform, we provide a $5.83$-approximation algorithm for the $δ$-minimum value and a $7.47$-approximation for the $δ$-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding ''adaptivity'' gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties. |
| title | Identifying Approximate Minimizers under Stochastic Uncertainty |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2504.17019 |