Is there any way to use create an objective function of ordered output? It is structured in a similar way to multiclass classification in that there are more than 2 outputs, but unlike multiclass the structure of the target is ordered (eg very bad, bad, neutral, good very good) - so using a multiclass objective is not ideal here as you would lose the ordering information.
In a sense it is like a multiclass with a monotonic output (eg Prob[Very Bad] < Prob[Very Bad or Bad] < Prob[Very Bad or Bad or Neutral] < Prob[Very Bad or Bad or Neutral or Good] < Prob[Very Bad or Bad or Neutral or Good or Very Good] (=1)]
I have seen a similar request over on the github site Ordinal classification [wish list] #695 - however the user was pointed to use rank:pairwise - as I see it though rank:pairwise deals with ranking different records within a group of records whereas we ordinal models want to assign a probability to all the ranking options within a record.