Personalized emotion recognition provides an individual training model for each target user in order to mitigate the accuracy problem when using general training models collected from multiple users. Existing personalized speech emotion recognition research has a cold-start problem that requires a large amount of emotionally-balanced data samples from the target user when creating the personalized training model. Such research is difficult to apply in real environments due to the difficulty of collecting numerous target user speech data with emotionally-balanced label samples. Therefore, we propose the Robust Personalized Emotion Recognition Framework with the Adaptive Data Boosting Algorithm to solve the cold-start problem. The proposed framework incrementally provides a customized training model for the target user by reinforcing the dataset by combining the acquired target user speech with speech from other users, followed by applying SMOTE (Synthetic Minority Over-sampling Technique)-based data augmentation. The proposed method proved to be adaptive across a small number of target user datasets and emotionally-imbalanced data environments through iterative experiments using the IEMOCAP (Interactive Emotional Dyadic Motion Capture) database.