Supervised machine learning for several coefficient

I have a set of items that are each described by 10 precise numbers n1, .., n10. I would like to learn the coefficients k1, .., k10 that should be associated to those numbers to rank them according to my criteria.

In that purpose I created a web application (in php) that shows me two items and ask me which one should be ranked first (it gives the supervision to the machine learning).

My question : I can’t find a way to learn the ten coefficients at the same time for each case. Do you have any idea on what algorithm I could use ? (neural networks with all the 10 numbers in entry seem to be a good option because it would learn all the coefficient, but I don’t know what would be the output of this network as I would like to learn it by comparing the items two by two.)

Source: php

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