  Orthogonal statistical learning and double machine learning have emerged as
general frameworks for two-stage statistical prediction in the presence of a
nuisance component. We establish non-asymptotic bounds on the excess risk of
orthogonal statistical learning methods with a loss function satisfying a
self-concordance property. Our bounds improve upon existing bounds by a
dimension factor while lifting the assumption of strong convexity. We
illustrate the results with examples from multiple treatment effect estimation
and generalized partially linear modeling.
