When a self-adaptive system needs to adapt, it has to analyze the possible options for adaptation, i.e., the adaptation space. For systems with large adaptation spaces, this analysis process can be resource- and time-consuming. One approach to tackle this problem is using machine learning techniques to reduce the adaptation space to only the relevant adaptation options. However, existing approaches only handle threshold goals, while practical systems often need to address also optimization goals. To tackle this limitation, we propose a two-stage learning approach called Deep Learning for Adaptation Space Reduction (DLASeR). DLASeR applies a deep learner first to reduce the adaptation space for the threshold goals and then ranks these options for the optimization goal. A benefit of deep learning is that it does not require feature engineering. Results on two instances of the DeltaIoT artifact (with different sizes of adaptation space) show that DLASeR outperforms a state-of-the-art approach for settings with only threshold goals. The results for settings with both threshold goals and an optimization goal show that DLASeR is effective with a negligible effect on the realization of the adaptation goals. Finally, we observe no noteworthy effect on the effectiveness of DLASeR for larger sizes of adaptation spaces. © 2020 ACM.