Trajectory-Based Recommender Systems as Control Systems

Traditional Recommender Systems (RS) are primarily designed to maximize immediate user engagement, often by predicting short-term preferences through collaborative filtering or content-based analysis. However, many modern applications—such as educational platforms, tourism itineraries, and clinical pathways—require guiding users toward a specific long-term objective rather than just satisfying a momentary interest. The authors define these as Trajectory-Based Recommender Systems (TBRS), where the sequence of interactions is not just a byproduct of the system, but its central purpose.

The paper argues that the current fragmented approaches to long-term recommendation lack a coherent mathematical foundation. By viewing the user as a dynamical system whose state evolves over time, the authors propose using Control Theory (CT) to formalize the TBRS problem. In this view, the recommendation engine acts as a controller that steers the user from an initial state toward a target state. This approach allows for the use of established control techniques, such as Model Predictive Control (MPC), to optimize a sequence of recommendations over a finite horizon while accounting for constraints and system dynamics.

The authors demonstrate how this control-theoretic framework can be applied to Educational Recommender Systems (ERS). By defining a state-space representation where the user's knowledge or progress is the state variable, the system can iteratively solve an optimization problem to suggest the next best item (e.g., a learning module) that minimizes the distance to the target goal. This framework is inherently adaptive: as the user interacts with the system, their state is updated, and the controller re-optimizes the trajectory, ensuring the recommendations remain relevant to the user's evolving progress.