Undecidability of Underfitting in Learning Algorithms

Abstract: Using recent machine learning results that present an information-theoretic perspective on underfitting and overfitting, we prove that deciding whether an encodable learning algorithm will always underfit a dataset, even if given unlimited training time, is undecidable. We discuss the importance of this result and potential topics for further research, including information-theoretic and probabilistic strategies for bounding learning algorithm fit.