How to quantify ‘compute cost’ of training of xgboost model?
If you have the time on hand, you could simply measure the time taken for all combinations of hyper parameter values in a Grid Search, preferably with repetition. It's unlikely that any theoretical analytical expression will provide adequate accuracy for predicting the compute cost, as there as so many factors that contribute noise to the compute time.
You could even build a regression model to predict the computing cost of new hyper parameter combinations if you wanted to.