arXiv:2607.15229v1 Announce Type: new 
Abstract: We develop data-driven algorithms for maintaining $N$ independent identical machines under a \textit{block replacement policy}, in which each machine is replaced upon failure and all machines are jointly replaced at regular intervals of length $k$. The goal is to learn the cost-minimizing interval $k^*$ from operational data when the lifetime distribution is unknown. At each decision epoch, the operator selects $k \in \{1, 2, \ldots, K\}$, observes the resulting failure history (a mixture of complete and right-censored lifetimes) and incurs a per-unit-time cost governed by the renewal function. We formulate this as a stochastic multi-armed bandit and propose Hoeffding- and Bernstein-based lower-confidence-bound algorithms achieving $O(K \log T)$ regret, matching the Lai--Robbins lower bound. Exploiting a nested observation property unique to block replacement, correlated variants attain $O((K-k^*)\log T)$ regret and require only $O(1)$ direct pulls of suboptimal arms $k < k^*$. A complementary Kaplan--Meier renewal algorithm estimates the lifetime distribution nonparametrically from censored data, achieving almost-sure policy consistency and empirically near-zero incremental regret at long horizons. We additionally analyze two average-cost MDPs: a time-elapsed formulation establishing that block replacement is optimal within its policy class for any lifetime distribution, and an age-vector formulation proving a monotone threshold structure under increasing failure rate distributions and providing a gold-standard cost benchmark. Numerical experiments confirm the theoretical ordering and reveal structural cost gaps between optimal block and age-dependent replacement.

قدمت دراسة جديدة خوارزميات مدفوعة بالبيانات لإدارة الآلات المستقلة المتطابقة بموجب سياسة استبدال الكتل، مع التركيز على تحديد فترة الاستبدال المثلى استنادًا إلى البيانات التشغيلية. تصيغ البحث هذا التحدي كمشكلة عصابة متعددة الأذرع عشوائية، مقترحة خوارزميات تحقق ندمًا يتطابق مع الحد الأدنى لـ Lai–Robbins.

Un nuevo estudio ha presentado algoritmos impulsados por datos para gestionar máquinas independientes idénticas bajo una política de reemplazo por bloques, centrándose en determinar el intervalo de reemplazo óptimo basado en datos operativos. La investigación formula este desafío como un problema de bandido multi-brazo estocástico, proponiendo algoritmos que logran un arrepentimiento que coincide con el límite inferior de Lai–Robbins.

Une nouvelle étude a introduit des algorithmes basés sur les données pour la gestion de machines indépendantes identiques selon une politique de remplacement par blocs, en se concentrant sur la détermination de l'intervalle de remplacement optimal basé sur des données opérationnelles. La recherche formule ce défi comme un problème de bandit manchot stochastique, proposant des algorithmes qui atteignent un regret correspondant à la limite inférieure de Lai–Robbins.

A new study has introduced data-driven algorithms for managing independent identical machines under a block replacement policy, focusing on determining the optimal replacement interval based on operational data. The research formulates this challenge as a stochastic multi-armed bandit problem, proposing algorithms that achieve regret matching the Lai–Robbins lower bound.