An effective framework for estimating individualized treatment rules

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and L 1 -penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while L 1 -penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent. Our comprehensive theoretical analysis reveals that weights that balance the spectrum of a 'weighted design matrix' improve both the optimization and likelihood landscapes, yielding improved computational and statistical estimation guarantees. In particular, this is achieved by distributional covariate balancing weights, which are model-free alternatives to IPW. Extensive simulations and applications demonstrate that our framework achieves significant gains in both robustness and effectiveness for ITR learning against existing methods. Contributions. We summarize our contributions below. • Unified Framework of ITR-Learning: We introduce a novel framework that addresses the limitations of existing ITR estimation methods by formulating the problem as a constrained, weighted, and smooth convex optimization problem. Under the framework, we propose a PGD algorithm for ITR-Learning under a hard L 1 -constraint. • Improved Computational and Statistical Guarantees: We establish convergence guarantees (Theorem 3.3). Furthermore, under mild assumptions, we demonstrate that the parameter of ITR-Learning can be consistently estimated with high probability (Theorem 3.5) and provide computational and sample complexity. In both cases, we demonstrate that using covariate balancing weights controls confounding factors and leads to better optimization and likelihood landscapes, resulting in improved computational and statistical performance. • Statistical Framework of ITR-Learning: Our main contribution lies in providing a unified framework that combines DCBWs, variable screening, outcome augmentation, and inverse variance weighting in a synergistic and effective way. We demonstrated theoretical justifications for the combined approach, which, to our knowledge, have not been previously established.