Efficient data compression is crucial for the storage and transmission of visual data. However, in facial expression recognition (FER) tasks, lossy compression often leads to feature degradation and reduced accuracy. To address these challenges, this study proposes an end-to-end model designed to preserve critical features and enhance both compression and recognition performance. A custom loss function is introduced to optimize the model, tailored to balance compression and recognition performance effectively. This study also examines the influence of varying loss term weights on this balance. Experimental results indicate that fine-tuning the compression model alone improves classification accuracy by 0.71% and compression efficiency by 49.32%, while joint optimization achieves significant gains of 4.04% in accuracy and 89.12% in efficiency. Moreover, the findings demonstrate that the jointly optimized classification model maintains high accuracy on both compressed and uncompressed data, while the compression model reliably preserves image details, even at high compression rates.