A Dynamical System Model for Knowledge Evolution and Exploration of User Trajectories in Recommender Systems

Modeling the dynamic evolution of user interests from sequential interaction data is a fundamental challenge in knowledge discovery and recommender systems. While exploring user preferences is crucial for improving experiences in recommender systems, it requires systematically modeling the sequential evolution of knowledge regarding individual user preferences. To that end, it is important to provide sufficient support for temporal dynamics and personalization when selecting and recommending appropriate exploratory content. In addition, it is beneficial to capture the long-term impact, besides immediate benefits, of exploratory items on future user behaviors. However, traditional exploration-oriented models struggle to capture the continuity of these interactions, suffering from feedback-loop biases that limit the system's ability to discover new knowledge. To address this research gap, we formulate recommendations as a user trajectory learning task in this paper, and propose Forward-looking Dynamical System Recommender (FDSR), a new exploratory recommendation method that determines these trajectory points based on dynamical system theory, where we utilize Ordinary Differential Equations (ODEs) to model the latent state transitions of the user preference. By numerically solving dynamical system equations designed to capture the user's desire for exploration, we produce the next point on the evolution trajectory and recommend items based on this predicted point. Theoretically, this formulation allows us to analyze the stability of interest evolution, providing a robust framework for handling sparse temporal data. Extensive offline experiments on three real-world datasets demonstrate significant performance improvements of FDSR over state-of-the-art baselines for both exploration and exploitation metrics. A simulation study further illustrates its long-term benefits across multiple rounds of interactions, and a large-scale online A/B test at a leading video streaming platform shows that the FDSR method significantly outperforms the latest production model. As a result, it has since been deployed in production.