PolyStepOR: Learning to Decide Without Optimal Decisions

Abstract:Decision-focused learning (DFL) trains predictors for downstream decision quality, but often relies on optimal reference decisions that are expensive to obtain. We present PolyStepOR, which trains directly from realized decision costs without pre-computed optima and extends to in-constraint predictions through repair or infeasibility penalties. To handle piecewise-constant losses, PolyStepOR perturbs predictor parameters, evaluates the resulting decisions, and uses optimal transport to favor lower-cost directions, requiring no derivatives. Without task-specific tuning, PolyStepOR performs strongly on classical optimization benchmarks and competitively on predicted-constraint and real-world problems. Theoretically, we characterize decision-preserving perturbations and boundary detection, bound sensitivity to cost errors, and establish stationarity guarantees for a smoothed objective. PolyStepOR thus replaces optimal reference decisions and derivatives with forward evaluations.

Machine Learning (cs.LG)

arXiv:2609.32465 [cs.LG]

(or arXiv:2609.32465v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32465 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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