Constraints on Causal Inference as Experiment Comparison: A Framework for Identification, Transportability, and Policy Learning

We introduce a decision-theoretic framework for causal inference derived from Le Cam's theory of statistical experiments. We define the \textbf{causal deficiency} $\delta(\mathcal{E}_{obs}, \mathcal{E}_{do})$ as the minimum information loss when simulating interventional experiments from observational data. Our contributions are two-fold. First, we prove that classical identification criteria (back-door, front-door) correspond to zero-deficiency conditions, and we derive \textbf{policy regret bounds} establishing that positive deficiency fundamentally limits the safety of causal decision-making ($\text{Regret}_{do} \le \text{Regret}_{obs} + 2\delta$). Second, we develop a constructive \textbf{deficiency diagnostic} using negative controls, enabling the quantification of unmeasured confounding from finite samples. We provide finite-sample learning bounds for these estimators. This framework bridges identification theory and statistical learning, providing a rigorous foundation for partial identification. We validate the theory on classical benchmarks (Lalonde, RHC) using the open-source R package \texttt{causaldef}.