Safe Deep Reinforcement Learning for Resource Allocation with Peak Age of Information Violation Guarantees

In Wireless Networked Control Systems (WNCSs), control and communication systems must be co-designed due to their strong interdependence. This paper presents a novel optimization theory-based safe deep reinforcement learning (DRL) framework for ultra-reliable WNCSs, ensuring constraint satisfaction while optimizing performance, for the first time in the literature. The approach minimizes power consumption under key constraints, including Peak Age of Information (PAoI) violation probability, transmit power, and schedulability in the finite blocklength regime. PAoI violation probability is uniquely derived by combining stochastic maximum allowable transfer interval (MATI) and maximum allowable packet delay (MAD) constraints in a multi-sensor network. The framework consists of two stages: optimization theory and safe DRL. The first stage derives optimality conditions to establish mathematical relationships among variables, simplifying and decomposing the problem. The second stage employs a safe DRL model where a teacher-student framework guides the DRL agent (student). The control mechanism (teacher) evaluates compliance with system constraints and suggests the nearest feasible action when needed. Extensive simulations show that the proposed framework outperforms rule-based and other optimization theory based DRL benchmarks, achieving faster convergence, higher rewards, and greater stability.