DePICT: Decision-Preserving Interface for Constrained Downstream Tasks

A constrained optimization problem may involve a parameter in its objective and in every active constraint, and yet its solution may be insensitive to small changes in that parameter. This raises a fundamental question: which inputs does a decision truly depend on? Building on this question we introduce DePICT, a procedure that constructs decision-preserving interfaces by ranking context directions with the optimizer's solution-sensitivity and aggregating them across an operating regime. We study this problem in a high-dimensional setting where primitive context parameterizes a constrained task and the downstream agent observes only a selected subset of context directions. For locally regular constrained programs, we derive a Karush–Kuhn–Tucker (KKT) based characterization of when a context direction is optimizer-relevant. Our analysis shows that appearing in the active optimization problem does not necessarily mean that a variable affects the final decision. Some context directions can change the KKT conditions while leaving the optimal solution unchanged because their effect is absorbed by the dual variables. DePICT is designed to remove exactly these directions. In a controlled diagnostis, it recovers the decision-relevant interface exactly and reduces linear-predictor regret from $0.475$ to $0.009$. It also performs well on controlled KKT-regime and real solver-mediated tasks.