Regularizing Extrapolation in Causal Inference

The academic paper proposes a new method for **regularizing extrapolation in causal inference** by replacing the common hard non-negativity constraints on estimation weights with a **soft penalty on negative weights**. This framework introduces a **"bias-bias-variance" tradeoff**, which explicitly accounts for biases arising from feature imbalance, model misspecification due to reliance on parametric assumptions during extrapolation, and estimator variance. The authors develop an optimization procedure to minimize a derived worst-case extrapolation error bound and demonstrate the effectiveness of their approach through synthetic experiments and a real-world application involving the **generalization of randomized controlled trial estimates** to an underrepresented target population. Ultimately, the work advocates for a more nuanced, continuous spectrum of regularization to handle positivity violations and high-dimensional data in causal estimation.