With the rapid growth in multimedia services and the enormous offers of video contents in online social networks, users have difficulty in obtaining their interests. Therefore, various personalized recommendation systems have been proposed. However, they ignore that the accelerated proliferation of social media data has led to the big data era, which has greatly impeded the process of video recommendation. In addition, none of them has considered both the privacy of users' contexts (e,g., social status, ages and hobbies) and video service vendors' repositories, which are extremely sensitive and of significant commercial value. To handle the problems, we propose a cloud-assisted differentially private video recommendation system based on distributed online learning. In our framework, service vendors are modeled as distributed cooperative learners, recommending videos according to user's context, while simultaneously adapting the video-selection strategy based on user-click feedback to maximize total user clicks (reward). Considering the sparsity and heterogeneity of big social media data, we also propose a novel geometric differentially private model, which can greatly reduce the performance (recommendation accuracy) loss. Our simulation shows the proposed algorithms outperform other existing methods and keep a delicate balance between computing accuracy and privacy preserving level.