Linear-programming-based recommender with personalized diversity constraints

A computerized method comprising:

• accessing a first set comprising pieces of content;
• executing a machine learning relevance model to provide a score for each piece of content in the first set;
• ranking pieces of content in the first set based on the scores;
• accessing a two-sided diversity constraint, the two-sided diversity constraint having an upper bound and a lower bound for a first attribute of the pieces of content;
• reducing the two-sided diversity constraint to a one-sided diversity constraint by eliminating either the upper bound or the lower bound;
• adding a dual variable to the one-sided diversity constraint;
• defining a dual objective function using the one-sided diversity constraint;
• producing a solution to the dual objective function using a bisection method;
• recovering a primal solution from the solution;
• and
• re-ranking the pieces of content in the first set based on the primal solution;
• causing display of one or more pieces of content in the first set based on the re-ranking.

A system comprising:

• means for accessing a first set comprising pieces of content;
• means for executing a machine learning relevance model to provide a score for each piece of content in the first set;
• means for ranking pieces of content in the first set based on the scores;
• means for accessing a two-sided diversity constraint, the two-sided diversity constraint having an upper bound and a lower bound for a first attribute of the pieces of content;
• means for reducing the two-sided diversity constraint to a one-sided diversity constraint by eliminating either the upper bound or the lower bound;
• means for adding a dual variable to the one-sided diversity constraint;
• means for defining a dual objective function using the one-sided diversity constraint;
• means for producing a solution to the dual objective function using a bisection method;
• means for recovering a primal solution from the solution;
• and
• means for re-ranking the pieces of content in the first set based on the primal solution;
• means for causing display of one or more pieces of content in the first set based on the re-ranking.