As machine learning (ML) technologies continue to evolve, there is an increasing demand for data. Mobile crowd sensing (MCS) can motivate more users in the data collection process through reasonable compensation, which can enrich the data scale and coverage. However, nowadays, users are increasingly concerned about their privacy and are unwilling to easily share their personal data. Therefore, protecting privacy has become a crucial issue. In ML, federated learning (FL) is a widely known privacy‐preserving technique where the model training process is performed locally by the data owner, which can protect privacy to a large extent. However, as the model size grows, the weak computing power and battery life of user devices are not sufficient to support training a large number of models locally. With mobile edge computing (MEC), user can offload some of the model training tasks to the edge server for collaborative computation, allowing the edge server to participate in the model training process to improve training efficiency. However, edge servers are not fully trusted, and there is still a risk of privacy leakage if data is directly uploaded to the edge server. To address this issue, we design a local differential privacy (LDP) based data privacy‐preserving algorithm and a deep reinforcement learning (DRL) based task offloading algorithm. We also propose a privacy‐preserving distributed ML framework for MEC and model the cloud‐edge‐mobile collaborative training process. These algorithms not only enable effective utilization of edge computing to accelerate machine learning model training but also significantly enhance user privacy and save device battery power. We have conducted experiments to verify the effectiveness of the framework and algorithms.