arXiv：cs.LG· Vahe Karagulyan, Miko{\l}aj Kasprzak, Pierre Alquier·· 2 小时前
连续 Markov 链伪谱间隙的 Minimax 估计及其经验集中不等式应用
Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds
AI 导读
研究团队提出一种针对紧致连续状态空间 Markov 链的伪谱间隙 γ_ps 的 Minimax 估计器。
正文
Abstract:We study the minimax estimation of the pseudo-spectral gap $\gamma_{ps}$ of a Markov chain from the observation of a single trajectory. Extending earlier works on finite-state space chains by Wolfer and Kontorovich (2024), we provide an estimator in the case of a compact, continuous state-space. Our estimator appears to be minimax-optimal on the class of chains with a transition operator with Lipschitz density, up to logarithmic terms. Our estimator, combined with Paulin's version of Bernstein inequality, allows to derive empirical concentration inequalities for Markov chains. This unlocks many applications, from confidence intervals, to active learning and generalization bounds. In particular, for rested bandits with Markov rewards, we provide a version of UCB with a regret bound similar to the one in the iid case, without assuming any knowledge on the pseudo-spectral gap of the chains.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST) |
| Cite as: | arXiv:2610.20007 [stat.ML] |
| (or arXiv:2610.20007v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20007 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Pierre Alquier [view email]
[v1]
Wed, 14 Oct 2026 11:22:54 UTC (41 KB)
来源：arXiv：cs.LG · arxiv.org