Do any optimization methods exist for ranking that ensure group gets target exposure in top K?

Question

Let’s say I already have a ranking method (a learning to rank approach) to sort search results (items) based on their utility to user. However, I also want to make sure certain groups of items get enough exposure across all the searches. I have defined target exposure for each group but I’m struggling to find a method that would balance utility and this exposure. Particularly because utility can be defined for a given search and item, but the group target exposure is only defined for an aggregated set of search results. Any ideas for a multi objective optimization method or even a post hoc re-ranking approach?