Orthogonal Statistical Learning with Self-Concordant Loss

TL;DR

This paper develops non-asymptotic bounds for orthogonal statistical learning with self-concordant loss functions, improving existing bounds by a dimension factor and removing the need for strong convexity, with applications in treatment effect estimation.

Contribution

It introduces non-asymptotic excess risk bounds for orthogonal learning methods using self-concordant losses, extending the theoretical understanding and applicability.

Findings

Bounds improve upon existing results by a dimension factor

Lifts the assumption of strong convexity in analysis

Applicable to treatment effect estimation and generalized partially linear models

Abstract

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.