Mobile edge computing (MEC) is a prominent computing paradigm which expands the application fields of wireless communication. Due to the limitation of the capacities of user equipments and MEC servers, edge caching (EC) optimization is crucial to the effective utilization of the caching resources in MEC-enabled wireless networks. However, the dynamics and complexities of content popularities over space and time as well as the privacy preservation of users pose significant challenges to EC optimization. In this paper, a privacy-preserving distributed deep deterministic policy gradient (P2D3PG) algorithm is proposed to maximize the cache hit rates of devices in the MEC networks. Specifically, we consider the fact that content popularities are dynamic, complicated and unobservable, and formulate the maximization of cache hit rates on devices as distributed problems under the constraints of privacy preservation. In particular, we convert the distributed optimizations into distributed model-free Markov decision process problems and then introduce a privacy-preserving federated learning method for popularity prediction. Subsequently, a P2D3PG algorithm is developed based on distributed reinforcement learning to solve the distributed problems. Simulation results demonstrate the superiority of the proposed approach in improving EC hit rate over the baseline methods while preserving user privacy.