Non-Asymptotic Analysis of (Sticky) Track-and-Stop
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912910835449856 |
|---|---|
| author | Poiani, Riccardo Bernasconi, Martino Celli, Andrea |
| author_facet | Poiani, Riccardo Bernasconi, Martino Celli, Andrea |
| contents | In pure exploration problems, a statistician sequentially collects information to answer a question about some stochastic and unknown environment. The probability of returning a wrong answer should not exceed a maximum risk parameter $δ$ and good algorithms make as few queries to the environment as possible. The Track-and-Stop algorithm is a pioneering method to solve these problems. Specifically, it is well-known that it enjoys asymptotic optimality sample complexity guarantees for $δ\to 0$ whenever the map from the environment to its correct answers is single-valued (e.g., best-arm identification with a unique optimal arm). The Sticky Track-and-Stop algorithm extends these results to settings where, for each environment, there might exist multiple correct answers (e.g., $ε$-optimal arm identification). Although both methods are optimal in the asymptotic regime, their non-asymptotic guarantees remain unknown. In this work, we fill this gap and provide non-asymptotic guarantees for both algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Asymptotic Analysis of (Sticky) Track-and-Stop Poiani, Riccardo Bernasconi, Martino Celli, Andrea Machine Learning In pure exploration problems, a statistician sequentially collects information to answer a question about some stochastic and unknown environment. The probability of returning a wrong answer should not exceed a maximum risk parameter $δ$ and good algorithms make as few queries to the environment as possible. The Track-and-Stop algorithm is a pioneering method to solve these problems. Specifically, it is well-known that it enjoys asymptotic optimality sample complexity guarantees for $δ\to 0$ whenever the map from the environment to its correct answers is single-valued (e.g., best-arm identification with a unique optimal arm). The Sticky Track-and-Stop algorithm extends these results to settings where, for each environment, there might exist multiple correct answers (e.g., $ε$-optimal arm identification). Although both methods are optimal in the asymptotic regime, their non-asymptotic guarantees remain unknown. In this work, we fill this gap and provide non-asymptotic guarantees for both algorithms. |
| title | Non-Asymptotic Analysis of (Sticky) Track-and-Stop |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.22475 |