Root Mean Squared Error (RMSE) and Root Mean Squared Logarithmic Error (RMSLE) both are the techniques to find out the difference between the values predicted by your machine learning model and the actual values.

To understand these concepts and their differences, it is important to know what does Mean Squared Error (MSE) mean. MSE incorporates both the variance and the bias of the predictor. RMSE is the square root of MSE. In case of unbiased estimator, RMSE is just the square root of variance, which is actually Standard Deviation.

Note: Square root of variance is standard deviation.

In case of RMSLE, you take the log of the predictions and actual values. So basically, what changes is the variance that you are measuring. I believe RMSLE is usually used when you don't want to penalize huge differences in the predicted and the actual values when both predicted and true values are huge numbers.

1. If both predicted and actual values are small: RMSE and RMSLE is same.
2. If either predicted or the actual value is big: RMSE > RMSLE
3. If both predicted and actual values are big: RMSE > RMSLE (RMSLE becomes almost negligible)