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In this paper, a deep reinforcement learning (DRL)-based approach to theLyapunov optimization is considered to minimize the time-average penalty whilemaintaining queue stability. A proper construction of state and action spacesis provided to form a proper Markov decision process (MDP) for the Lyapunovoptimization. A condition for the reward function of reinforcement learning(RL) for queue stability is derived. Based on the analysis and practical RLwith reward discounting, a class of reward functions is proposed for theDRL-based approach to the Lyapunov optimization. The proposed DRL-basedapproach to the Lyapunov optimization does not required complicatedoptimization at each time step and operates with general non-convex anddiscontinuous penalty functions. Hence, it provides an alternative to theconventional drift-plus-penalty (DPP) algorithm for the Lyapunov optimization.The proposed DRL-based approach is applied to resource allocation in edgecomputing systems with queue stability and numerical results demonstrate itssuccessful operation.

A Reinforcement Learning Formulation of the Lyapunov Optimization: Application to Edge Computing Systems with Queue Stability