US Patent 11551280 Method, manufacture, and system for recommending items to users

In various embodiments, a training application generates a preference prediction model based on an interaction matrix and a closed-form solution for minimizing a Lagrangian. The interaction matrix reflects interactions between users and items, and the Lagrangian is formed based on a constrained optimization problem associated with the interaction matrix. A service application generates a first application interface that is to be presented to the user. The service application computes predicted score(s) using the preference prediction model, where each predicted score predicts a preference of the user for a different item. The service application then determines a first item from the items to present to the user via an interface element included in the application interface. Subsequently, the service application causes a representation of the first item to be displayed via the interface element included in the application interface.