A common challenge in personalized user preference prediction is the cold-start problem. Due to the lack of user-item interactions, directly learning from the new users' log data causes serious over-fitting problem. Recently, many existing studies regard the cold-start personalized preference prediction as a few-shot learning problem, where each user is the task and recommended items are the classes, and the gradient-based meta learning method (MAML) is leveraged to address this challenge. However, in real-world application, the users are not uniformly distributed (i.e., different users may have different browsing history, recommended items, and user profiles. We define the major users as the users in the groups with large numbers of users sharing similar user information, and other users are the minor users), existing MAML approaches tend to fit the major users and ignore the minor users. To address the task-overfitting problem, we propose a novel personalized adaptive meta learning approach to consider both the major and the minor users with three key contributions: 1) We are the first to present a personalized adaptive learning rate meta-learning approach to improve the performance of MAML by focusing on both the major and minor users. 2) To provide better personalized learning rates for each user, we introduce a similarity-based method to find similar users as a reference and a tree-based method to store users' features for fast search. 3) To reduce the memory usage, we design a memory agnostic regularizer to further reduce the space complexity to constant while maintain the performance. Experiments on MovieLens, BookCrossing, and real-world production datasets reveal that our method outperforms the state-of-the-art methods dramatically for both the minor and major users.