**Abstract**

This chapter introduces a dynamic and low-complexity decision-making algorithm which aims at time-average utility maximization in real-time deep learning platforms, inspired by Lyapunov optimization. In deep learning computation, large delays can happen due to the fact that it is computationally expensive. Thus, handling the delays is an important issue for the commercialization of deep learning algorithms. In this chapter, the proposed algorithm observes system delays at first formulated by queue-backlog, and then it dynamically conducts sequential decisionmaking under the tradeoff between utility (i.e., deep learning performance) and system delays. In order to evaluate the proposed decision-making algorithm, the performance evaluation results with real-world data are presented under the applications of super-resolution frameworks. Lastly, this chapter summarizes that the Lyapunov optimization algorithm can be used in various emerging applications.

**Keywords:** Lyapunov optimization, stochastic optimization, real-time computing, deep learning platforms, computer vision platforms
