I'm searching for a loss function that fits my Project. Actually I have two question but they are in the same direction. I take a look at the definition of the root mean squared error and the euclidean distance and they look the same to me! that's why I want to know what's the difference between the two. what would be the difference if I use rmse as a loss function or the euclidean distance??
the second question is how to search for a loss function. I mean I know it depends on the problem and commun things are MSE for Regression and Cross entropy for Classification but let's say I have a specific problem, how do I search for a loss function? I also saw that some people use a custom loss function and most of the deep learning frameworks allows us to define a custom loss function but why would I want to use a custom one? how I get the intuition that I need a custom loss function?
now to explain my problem. I'm doing a project where I need to reduce the GPS Error of a vehicle (I have some vehicle data and my neural network will try to predict the longitude and latitude so it's a regression problem) that's why I get the Idea of maybe the euclidean distance would make sense as a loss function, right? now somehow MSE also make sense to me because it is getting the difference between prediction and ground truth. does this make sense to you as a professional ML Engineer or Data scientist ? and if there would be a custom loss function that you can use, what would you suggest and why?