Ultra-Dense Networks (UDNs) is widely considered as a key technology of fifth generation (5G) networks, where access points (APs) are densely deployed to meet the high capacity requirements in various environments. However, the large scale of UDNs inevitably increases the computational complexity and signaling overhead for resource allocation processes. In this paper, employing discrete power levels, we propose a stochastic geometry based hierarchical power allocation scheme to maximize the user sum rate in uplink UDNs. Using stochastic geometry theory, we first group all users in terms of their transmit powers, and then derive two key metrics including statistical information-based signal to interference and noise ratio (SSINR) and the lower bound of statistical information-based user rate (SR). Furthermore, an alternative genetic algorithm (AGA) is utilized to obtain the power allocation scheme. Simulation results show that the proposed power allocation algorithm is not only able to improve the user sum rate, but also can significantly reduce the signaling overhead and computation complexity.