Weak-to-Strong Learning Improves Contextual Decision Models

Many operational decisions rely on predictive models that estimate uncertain outcomes, but training these models often faces a fundamental challenge: labeled data is scarce and expensive, while contextual covariates are abundant. This paper addresses this data asymmetry by proposing a "decision-aware weak-to-strong (W2S)" learning framework. The W2S framework operates by first training a "weak" model using the limited labeled data. This weak model then generates predicted outcome distributions for the plentiful unlabeled contexts, providing a form of "soft supervision" for training a more powerful "strong" model. The research provides theoretical guarantees, establishing non-asymptotic upper bounds on the excess decision risk for W2S and comparing them to a strong-only benchmark. It identifies explicit conditions under which W2S improves decision performance, notably when the correlation dimension between the weak and strong feature representations is small. Empirical evidence from a synthetic newsvendor experiment and a real-world comment moderation task supports the theory, demonstrating the framework's ability to reduce the impact of teacher errors using unlabeled data.