Question: I am modelling a regression with a GBM and evaluate by RMSE. My model input & target is log-transformed which results in an RMSE that is also on log-scale.

How can i interpret this in an intuitive way, e.g. as deviation from the mean price or sth. equal, that is easy to understand?

Answer: 
As the RMSE is in log-space it behaves like a multipicative factor. So you are finding the square root of the mean of the squared ratio between the model values and the true values.

I.e. if the RMSE were 0.693 (=ln 2) the model values would be roughly a factor of two out on average (in either direction) from the true values in the original (non-log) space.

Also, by taking the mean in log space you are less sensitive to large valued outliers.
great answer by @stuart10 above. I'd like to add that if you transform your `y_pred` and `y` variables back from logspace (say, using `np.exp`) you can in addition calculate RMSE where the results is the mean error in the original units.

so if `y` was in dollars, after transforming back from logspace, RMSE would give average error in dollars