# A Comprehensive Survey of Recommender Systems Based on Deep Learning
## 3 Overview of the Recommender Systems
### Sequential Recommendation
#### 3.2.3 Multi-Objective Sequence Recommendation
\[masked\_soft\text{max}(h_{t},E,m_{t})_{j}=\frac{\exp(h_{t}^{T}e_{j}-m_{t,j})}{ \sum_{j=1}^{N}\exp(h_{t}^{T}e_{j}-m_{t,j})} \tag{13}\]  
Specifically, the beam search retains the top k most promising candidate bundle lists in each step and subsequently extends these lists in the next step to progressively construct longer recommended bundle lists. This paper employed a beam search to generate more accurate and relevant bundle recommendation lists while also ensuring the computational efficiency of the model. After all, with the continual advancements achieved in deep learning and natural language processing technologies, sequential recommender systems are well-primed for further optimization and development. More advanced model architectures, such as transformers and BERT, can be employed to capture complex sequential patterns. Moreover, integrating these techniques with other recommendation approaches, such as those based on knowledge graphs, may enhance both the diversity and accuracy of sequential recommender systems. As the Internet of Things and smart home technologies continue to proliferate, the utilization of sequential recommendation is expected to further broaden in everyday life. Recent research on sequential recommendation remains highly active, with some researchers considering temporal information in sequential recommendation [105]. They aggregate sequential information and collaborative signals in user behavior sequences, thereby taking a more comprehensive approach to considering the information in sequential behaviors. In order to enhance the transition probabilities between items in sequences, researchers employ contrastive learning for sequential recommendation [106]. They introduce two informative augmentation operators leveraging item correlations to create high-quality views for contrastive learning. Traditionally, recommender systems have often employed static strategies to characterize the interactions between users and items, relying on long-term historical behaviors to infer user interests. However, the selection of a particular item by a user is not solely based on their long-term stable preferences but is increasingly driven by their fluctuating short-term interests [107]. In fact, user interests dynamically evolve over time. This is precisely where sequential recommendation comes into play. Sequential recommendation models the user-product interaction history as a dynamic sequence and utilizes the temporal dependencies within this sequence to capture the evolving user preferences, leading to more precise and timely recommendations. Deep learning enables the hierarchical treatment of complex problems, swiftly identifying the latent patterns and relationships between different layers of data. The integration of deep learning with a sequential recommendation can also adjust recommendations based on dynamic user preference changes, further enhancing their effectiveness [108]. Sequential recommender systems excel at accurately predicting users' immediate interests and dynamically adapting to their behavior changes and shifting preferences. This approach not only guarantees content diversity but also furnishes recommendations that are highly pertinent to users' recent activities, even if these suggestions may not fully correspond with users' earlier behavioral patterns. While sequential recommendation undoubtedly offers unique advantages, it is important to mention that handling time-series data can introduce additional computational demands on the model [109]. Furthermore, an undue emphasis on users' short-term actions carries its own set of risks, potentially leading to a neglect of their long-term interests and preferences.