Existing works in multimodal affective computing tasks, such as emotion recognition and personality recognition, generally adopt a two-phase pipeline by first extracting feature representations for each single modality with hand crafted algorithms, and then performing end-to-end learning with extracted features. However, the extracted features are fixed and cannot be further fine-tuned on different target tasks, and manually finding feature extracting algorithms does not generalize or scale well to different tasks, which can lead to sub-optimal performance. In this paper, we develop a fully end-to-end model that connects the two phases and optimizes them jointly. In addition, we restructure the current datasets to enable the fully end-to-end training. Furthermore, to reduce the computational overhead brought by the end-to-end model, we introduce a sparse cross-modal attention mechanism for the feature extraction. Experimental results show that our fully end-to-end model significantly surpasses the current state-of-the-art models based on the two-phase pipeline. Moreover, by adding the sparse cross-modal attention, our model can maintain the performance with around half less computation in the feature extraction part of the model.