Social recommendation has been an active research topic over the last decade, based on the assumption that social information from friendship networks is beneficial for improving recommendation accuracy, especially when dealing with cold-start users who lack sufficient past behavior information for accurate recommendation. However, it is nontrivial to use such information, since some of a person's friends may share similar preferences in certain aspects, but others may be totally irrelevant for recommendations. Thus one challenge is to explore and exploit the extend to which a user trusts his/her friends when utilizing social information to improve recommendations. On the other hand, most existing social recommendation models are non-interactive in that their algorithmic strategies are based on batch learning methodology, which learns to train the model in an offline manner from a collection of training data which are accumulated from users? historical interactions with the recommender systems. In the real world, new users may leave the systems for the reason of being recommended with boring items before enough data is collected for training a good model, which results in an inefficient customer retention. To tackle these challenges, we propose a novel method for interactive social recommendation, which not only simultaneously explores user preferences and exploits the effectiveness of personalization in an interactive way, but also adaptively learns different weights for different friends. In addition, we also give analyses on the complexity and regret of the proposed model. Extensive experiments on three real-world datasets illustrate the improvement of our proposed method against the state-of-the-art algorithms.