Primary Submission Category: Machine Learning and Causal Inference
From Iterative Targeting to One-Step Updates: Convex-Dual Affine Universal Least Favorable Models for Heterogeneity, Distributional, and Policy-Risk Estimands
Authors: Kaiwen HOU, Mark van der Laan,
Presenting Author: Kaiwen HOU*
Modern causal inference increasingly targets nonlinear estimands, for which valid inference with flexible nuisance learning relies on semiparametrically efficient procedures built around the efficient influence function (EIF). In practice, efficiency is often pursued via iterative local targeting in TMLE updates, repeatedly computing the EIF and taking small steps, which can be computationally costly and numerically unstable.
We identify a broad class of settings where the universal least favorable model (ULFM) admits a semi-explicit solution. The key structure is that the ULFM score equation reduces to an equation pointwise in the nuisance functions and coupled only through finitely many scalar moments (e.g., normalizing constants or low-order moments). We term these mean-field ULFMs. This structure yields one-step TMLE updates that enforce the EIF score condition without iterative recomputation, often requiring only the solution of a low-dimensional auxiliary ODE.
We derive mean-field ULFMs for: i) density functionals, including density power integrals and distributional treatment effect; ii) heterogeneity functionals, including centered moments of CATE; iii) policy risk functionals, including the variance of policy value; and iv) propensity and overlap functionals. Simulations show that ULFM-based one-step targeting can improve numerical stability and reduce sensitivity to step-size tuning relative to iterative local targeting while maintaining finite-sample performance.