arXiv：cs.LG· Nadav Sukenik, Nadav Merlis·· 4 小时前AI 评分33
多臂老虎机中的期望样本复杂度研究
Expected Sample Complexity in Multi-Armed Bandits
AI 导读
研究针对随机多臂老虎机问题提出"期望样本复杂度"性能指标，并在一套名为 ACE（approximately correct in expectation）的新框架下进行分析。
正文
Abstract:Sample complexity is a widely used metric in sequential decision-making problems, defined as the number of suboptimal decisions during the interaction between the agent and an environment. We study the sample complexity of stochastic multi-armed bandit problems and introduce the expected sample complexity performance measure, analyzing it in a novel framework called approximately correct in expectation (ACE). We show that ACE guarantees imply almost sure convergence to the optimal expected reward, in contrast to high-probability guarantees found in other frameworks, and also show how to convert ACE guarantees into explicit expected regret bounds. We further show that, in contrast to existing measures, deterministic algorithms cannot obtain favorable ACE bounds, and analyze stochastic algorithms in two settings: when the allowed suboptimality level $\epsilon$ is known to the algorithm and when it is unknown. In the former, we devise an explore-then-$\epsilon$-greedy algorithm, and in the latter, we analyze the expected sample complexity of Thompson sampling. Finally, we establish nearly matching lower bounds for both settings, showing that the algorithms are tight in $\epsilon$ and proving a performance separation between the two regimes.
| Subjects: | Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.09929 [cs.LG] |
| (or arXiv:2610.09929v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09929 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Nadav Merlis [view email]
[v1]
Wed, 7 Oct 2026 12:16:27 UTC (487 KB)
来源：arXiv：cs.LG · arxiv.org