How to perform Learning to Rank for a small dataset

I am very interested in applying Learning to rank to my problem doamin. When I read through the literature of Learning to rank I noted that the data they have used for training include thousands of queries.

However, in my problem domain I only have 6 use-cases (similar to 6 queries) where I would like to obtain a ranking function using machine learning. I know the data I have is very very small.

So, my question is; Can apply learning to rank in my problem? If not what are the other methods that I can use to make a ranking of my documents in each query.

I am happy to provide more details if needed.