Targeted Sequential Indirect Experiment Design
Elisabeth Ailer, Niclas Dern, Jason Hartford, Niki Kilbertus
TL;DR
This paper tackles the challenge of answering targeted causal questions when direct interventions are impractical and confounding obscures identification. It casts indirect experimentation as a sequential minimax instrumental-variable problem, aiming to bound a query $Q[f_0]$ of a nonlinear, multivariate mechanism by maintaining $Q^+(\pi)$ and $Q^-(\u0003\pi)$ and iteratively reducing the gap $\Delta(\pi)$. The authors derive closed-form estimators for these bounds under RKHS assumptions, and propose adaptive strategies to select experiments that best shrink the bound interval, including a gradient-based adaptive policy with a Gaussian mixture over instrument settings. The approach enables robust, data-efficient narrowing of uncertainty about targeted causal effects in settings with unobserved confounding and complex dependencies, with demonstrated success in synthetic experiments and clear pathways to real-world deployment with further theoretical and practical development. Overall, the work advances adaptive, indirect experimentation by combining minimax IV estimation, RKHS-based closed-form solutions, and sequential policy optimization to identify or tightly bound specific aspects of a system’s mechanism.
Abstract
Scientific hypotheses typically concern specific aspects of complex, imperfectly understood or entirely unknown mechanisms, such as the effect of gene expression levels on phenotypes or how microbial communities influence environmental health. Such queries are inherently causal (rather than purely associational), but in many settings, experiments can not be conducted directly on the target variables of interest, but are indirect. Therefore, they perturb the target variable, but do not remove potential confounding factors. If, additionally, the resulting experimental measurements are multi-dimensional and the studied mechanisms nonlinear, the query of interest is generally not identified. We develop an adaptive strategy to design indirect experiments that optimally inform a targeted query about the ground truth mechanism in terms of sequentially narrowing the gap between an upper and lower bound on the query. While the general formulation consists of a bi-level optimization procedure, we derive an efficiently estimable analytical kernel-based estimator of the bounds for the causal effect, a query of key interest, and demonstrate the efficacy of our approach in confounded, multivariate, nonlinear synthetic settings.