Never Go Full Batch: Stochastic TMLE for Large-Scale Debiased Inference

Targeted Minimum Loss-based Estimation (TMLE) is a classical plug-in debiasing methodology that delivers doubly robust estimation and asymptotically efficient inference. Despite its statistical guarantees, each iteration of standard TMLE requires solving a minimization subproblem over the entire dataset, resulting in prohibitive computational and memory costs that render the method impractical for large-scale or real-time settings. To ease the bottlenecks, we introduce stochastic TMLE, a randomized targeting procedure that replaces each expensive full-batch fluctuation fit with mini-batch alternatives. Our theoretical analysis establishes that the stochastic iterates converge to a neighborhood (noise ball) centered around the target solution, and crucially, only a small number of subsequent full-sample TMLE iterations suffice to reach an empirical efficient influence function root. Consequently, our stochastic variant inherits the same guarantees and attractive properties as classical TMLE while substantially reducing per-iteration complexity. We further propose two computational variants with provable guarantees that broaden the algorithmic design space, offering flexibility for future developments in scalable targeted learning. Extensive experiments across diverse regimes demonstrate substantial acceleration over standard TMLE without sacrificing inferential quality.