Adaptive Double Machine Learning via Riesz-Risk Cross-Validation

Standard double/debiased machine learning (DML) yields $\sqrt{n}$-valid inference by plugging machine-learned nuisances into a Neyman-orthogonal score, but applied work must pre-specify and tune first-stage learners. Many implementations use symmetric (coupled) pipelines that choose or tune both the regression nuisance $g$ and the debiasing function $\alpha$ using prediction criteria. Because prediction-optimal $g$ can be misaligned with the complexity of the associated Riesz representer, coupling can violate product-rate conditions and induce $\sqrt{n}$-scale drift. I develop Adaptive Riesz-DML, an end-to-end, data-driven estimator for continuous linear-functional targets. Leveraging the Riesz representation, the estimator selects $g$ by cross-validated mean-squared prediction loss and selects $\alpha$ by held-out quadratic Riesz risk, allowing distinct learner libraries and tuning rules. Model selection is nested inside cross-fitting, preserving orthogonality under data-driven choice. I establish a fast-rate oracle inequality for the Riesz-risk selector over growing libraries of learners and prove a fold-wise conditional second-order adaptive orthogonality identity for the selected nuisances. Under standard product-rate conditions, the estimator is asymptotically linear and attains the semiparametric efficiency bound. Simulations and a 401(k) application deliver more stable $\sqrt{n}$ confidence intervals than coupled pipelines in practice.