Edge serverless computing has been widely used in mobile and web applications thanks to its simplicity and cost efficiency of network resource management. Serverless functions, event-driven and often stateless, are deployed on edge servers to reduce the latency caused by data transfer and the workload on cloud servers. However, in many edge serverless application scenarios, such as in IoT networks, the network is usually hierar-chical, with limited edge storage and computational capacity, and requests received by different edge nodes might be heterogeneous and time-varying. The function deployment policy becomes a key issue in achieving guaranteed network performances. In this paper, we focus on function allocation policy in edge serverless computing networks to help edge nodes dynamically choose the functions to deploy based on incoming requests, aiming to reduce latency and minimize request outage rate. A Deep Deterministic Policy Gradient (DDPG)-based function allocation algorithm is proposed for a multi-tier edge-serverless computing scenario where a set of functions are deployed to the edge nodes strategically. Simulation results show that our proposed method can reduce the latency of requests while also minimizing the outage rate.