Multitask learning has proven to be useful in the field of machine learning when additional knowledge is available to help a prediction task. We adapt this paradigm to develop autotuning frameworks, where the objective is to find the optimal performance parameters of an application code that is treated as a black-box function. Furthermore, we combine multitask learning with multi-objective tuning and incorporation of coarse performance models to enhance the tuning capability. The proposed framework is parallelized and applicable to any application, particularly exascale applications with a small number of function evaluations. Compared with other state-of-the-art single-task learning frameworks, the proposed framework attains up to 2.8X better code performance for at least 80% of all tasks.