Weak-to-Strong Learning in Decision Making

Abstract:Many operational decisions rely on predictive models that estimate uncertain outcomes conditional on observable contexts. Training such models, however, often faces a fundamental data asymmetry: labeled outcomes are scarce or costly to obtain, while contextual covariates are abundant. Motivated by this data asymmetry, we develop a decision-aware weak-to-strong (W2S) framework that leverages both labeled and unlabeled data to improve contextual stochastic optimization. Specifically, we first train a weak model using limited labeled data and then use it to generate predicted outcome distributions on unlabeled contexts. These distributions provide soft supervision for training a strong model. We establish a non-asymptotic upper bound on the excess decision risk of W2S and a complementary lower bound for a strong-only benchmark. Their comparison yields explicit sufficient conditions under which W2S improves downstream decision performance. The key quantity is the correlation dimension between the weak and strong feature representations: when it is small, abundant unlabeled data reduce the effect of teacher errors along non-overlapping directions. A synthetic newsvendor experiment and a comment moderation experiment based on real-world data provide empirical evidence consistent with the theory.

Machine Learning (cs.LG)

arXiv:2607.18467 [cs.LG]

(or arXiv:2607.18467v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.18467 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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