# Cost-Aware Optimized Front-Door Experimental Design

arXiv: https://arxiv.org/abs/2603.22024 · HTML: https://mlsanity.com/paper/2603.22024/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [When Is Coarse Supervision Worth It? Cost-Aware Learning under Unknown Aggregation](https://mlsanity.com/paper/2609.36704/) (2026)

## Abstract (arXiv)

Causal effect estimation often succeeds cost-constrained sequential data collection. This work considers multivariate linear front-door models with arbitrary unobserved confounding on treatment and response. We optimize the experimental design by balancing the statistical efficiency and measurement costs through partial data. The full-data efficient influence function for the causal effect is derived, together with the geometry of all observed-data influence functions. This characterization yields a closed-form optimal sampling policy and an estimator to minimize the asymptotic variance of regular asymptotically linear (RAL) estimators within a class of augmented full-data influence functions. The resulting design also covers back-door estimation. In simulations and applications to biological, medical, and industrial datasets, the optimized designs achieve substantial efficiency gains (5.3% to 31.9%) over naive full-sampling strategies.