Computational algorithms for anticancer drug synergy prediction (ACDSP) have the potential to discover novel anticancer drug combinations. Most of the algorithms are based on deep learning (DL) and use chemical features of anticancer drugs and multiomic features of cancer cell lines. Deep tensor completion (DTC)-based ACDSP algorithms achieve similar performance to DL-based ACDSP algorithms without using chemical or multiomic features. However, current DTC-based ACDSP algorithms are trained in two separate steps, potentially limiting their performance. In this M.Sc. thesis, I develop a novel DTC-based ACDSP algorithm, named Deep Selective CANDECOMP/PARAFAC (DSCP), which can be trained in an end-to-end fashion. It was found that DSCP made significantly better performance on a synthetic tensor classification task, while using less resources than the non-end-to-end trainable version of DSCP. Furthermore, I also propose a new ACDSP algorithm that can utilize multimodal data fusion methods (e.g., intermediate fusion (IF)) to integrate tensor-based drug and cell line data with chemical and multiomic features, which is named SynergyIF. Finally, this thesis found evidence that many ACDSP algorithms do not utilize the chemical and biological structure of their input features, instead treating these features as unique identifiers. This was done by examining the effects of randomizing ACDSP algorithms’ input data on their predictive performance. Overall, although the thesis demonstrates some advantages to integrating deep learning and tensor completion algorithms in an end-to-end fashion, more work is warranted to fuse multimodal data under the learning framework.