Factorization Machines - how to recommend?


I am looking at methods for making product recommendations to customers based on attributes of the customer (e.g. demographics) and past product interactions (e.g. did or did not buy). There are many potential products to recommend. This is of course an implicit feedback recommendation engine setup.

If a model is built using a factorization machine, how does one go about recommendations?

Once a model is built…how to serve recommendations? Does one have to iterate through all the products (variants) for each customer? This seems prohibitive.

While this is described as a product recommendation, a click through model in adtech would be the other common situation. Wondering how people deal with this in the real world?