Smooth Multi-Policy Causal Effect Estimation in Longitudinal Settings

摘要

Comparative evaluation of *multiple* dynamic treatment policies is essential for healthcare and policy decisions, yet conventional longitudinal causal inference methods estimate each in *isolation*, preventing information sharing across counterfactuals. We demonstrate that this separate estimation paradigm induces a structurally uncontrolled second-order bias, inflating finite-sample variance even after standard debiasing with *longitudinal targeted maximum likelihood estimation* (LTMLE). To address this, we propose a policy-aware reparameterization of *Iterative Conditional Expectation* (ICE) Q-functions that enables joint estimation through shared representations. We implement this approach in the **Policy-Encoded Q Network (PEQ-Net)**, an architecture centered on a shared policy encoder. The encoder is trained using kernel mean embeddings, ensuring that the learned representation space reflects population-level policy dissimilarities. After applying an LTMLE correction step, we prove this design imposes a structural constraint on the second-order remainder, thereby stabilizing finite-sample variance. Experiments on semi-synthetic datasets demonstrate that PEQ-Net consistently outperforms existing ICE-based methods, reducing root-mean-square error by 13–62\%.