Optimize coefficients for multi variable linear regression of scoring metric

Question

I have ecommerce site which I try to optimize my search results to give the most relevant ones for the user.

To give the most relevant results for searches I made a rating metric. The rating metric is build based on the product parameters and the weight of each one.

• The rating score is normalized from 0-1

• The functions of fn returns score from 0-1

  rating = b0*f0(X0) + b0*f1(X1) + bn*fn(Xn)

e.g: rating = 0.4*f(seller_score) + 0.25*f(customers_stars) + 0.35*f(return_rate) = 0.683

When someone search for "kitchen chair" I sort the returned results based on the rating score.

SELECT 
 * 
FROM 
 db 
WHERE 
  category = "kitchen chair" 
ORDER BY rating DESC 
LIMIT 50

The user click on some results which I log. In optimal world the user will pick one of the first results since the rating score is working well and the user is getting what he probably was looking for. But if the user picked the 24th product from the list maybe my rating score is not optimized.

My goal is to optimize the coefficients of my rating metric to match as much as possible for what the users actually click on so they will get the best result first.

I have a series of n search terms with their results and what the user clicked on.

What algorithm I can use to find the best coefficients of b0, b1, ..bn so the clicked results will actually be on top. For now I look to find a result the fits for all the search term and not to optimize each search term.

Answer 1

What algorithm?

You are describing Learning to Rank. There is an extensive literature you can consult.