Join us on February 5th to continue our CTML Seminar Series! Kaiwen Hou will give his talk on "Hierarchical Approximation of Universal Least Favorable Paths for Improved Efficiency." This talk will take place at 12:00PM at Berkeley Way West, 5th Floor, Room 5401.
TMLE achieves efficiency by constructing paths in the statistical model space that solve the efficient score equation with minimal updates, where the universal least favorable path (UFLP) theoretically enables single-step convergence by exactly matching the canonical gradient at every point along the path, though constructing this path is intractable for many key causal parameters like the variance of CATE. We propose a hierarchy of approximate paths derived from perturbation expansions of the UFLP’s defining partial differential equation, beginning with the standard TMLE path that enforces a first-order condition only at the path’s initial measure, solving the efficient score equation up to O(||initial rate||^2), and showing that extending to second-order conditions dramatically reduces the remainder by explicitly minimizing a KL divergence, which corresponds to maximizing the Cramér–Rao lower bound. This second-order path, derived by imposing an expectation-based condition, is computationally tractable using standard convex-optimization routines, while an alternative second-order path imposes pointwise conditions, achieving O(||initial rate||^3) with minimal additional computational effort. Further extensions to higher-order local paths offer increasingly refined approximations of the UFLP, providing a theoretical pathway toward single-step TMLE with enhanced computational feasibility and performance in finite samples.