The GP service error message seems to point to the output folder when you run the inference. Assuming you have an imagery layer that you want to detect objects from, it will create hosted feature layer that contains these detected objects. For troubleshooting purpose, I would suggest a few steps:
1. Current user is a publisher
2. Check if the current user can create a hosted feature layer on Content page -> Add Item -> Hosted feature layer
3. Check that the image server with the RA role has a fileShare based raster store and there is no other type of raster stores (i.e. cloud raster store or database raster store)
4. Before you click the Start button, click the gear icon to bring up the environment settings. If you have dedicated NVIDIA GPU available on your RA server, you can use either GPU or CPU. Otherwise try switching to use CPU.
One additional palce to check is to make sure you have Deep Learning Libraries installed correctly. If you have been able to use Deep Learning Studio to browse to a model (DLPK) from your portal, it's a sign that DL libraries are installed.