The TrainingSetClient is a Python module wrapping a set of API methods. See Authentication for the default behavior of the TrainingSetClient.
To override authentication, you need to set the right environment variable with your own user API key:
import os
os.environ["DOMINO_USER_API_KEY"] = "<your-own-api-key>"
# In Domino endpoint if the client version is <0.1.8
os.environ["DOMINO_API_HOST"] = os.getenv("DOMINO_USER_HOST")