Boosted tree regression loss function when data has occasionally very large values to predict?
I am working almost on the same problem these days: 

I have tried two options using XGB Regression with different objective functions including:


Using a linear regression objectiive function ("reg:linear" or "reg:squarederror") and transformed the target to the log space
Using the gamma objective function ("reg:gamma"), which is useful for a skewed target with gamma distribution, e.g., insurance claims severity. In this case, I did not transform my target to the log space. 


You can try these two cases and see which one performs better. However, in my case, option 1 performed better than option 2 (around 15-20%).

Also, you can try "reg:squaredlogerror"