Ultra-reliable low-latency communication (URLLC) is the cornerstone for a broad range of emerging services in next-generation wireless networks. URLLC fundamentally relies on the network's ability to proactively determine whether sufficient resources are available to support the URLLC traffic, and thus, prevent so-called cell overloads. Nonetheless, achieving accurate quality-of-service (QoS) predictions for URLLC user equipment (UEs) and preventing cell overloads are very challenging tasks. This is due to dependency of the QoS metrics (latency and reliability) on traffic and channel statistics, users' mobility, and interdependent performance across UEs. In this paper, a new QoS-aware UE admission control approach is developed to proactively estimate QoS for URLLC UEs, prior to associating them with a cell, and accordingly, admit only a subset of UEs that do not lead to a cell overload. To this end, an optimization problem is formulated to find an efficient UE admission control policy, cognizant of UEs' QoS requirements and cell-level load dynamics. To solve this problem, a new machine learning based method is proposed that builds on (deep) neural contextual bandits, a suitable framework for dealing with nonlinear bandit problems. In fact, the UE admission controller is treated as a bandit agent that observes a set of network measurements (context) and makes admission control decisions based on context-dependent QoS (reward) predictions. The simulation results show that the proposed scheme can achieve near-optimal performance and yield substantial gains in terms of cell-level service reliability and efficient resource utilization.

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