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AAAI 2026

January 23, 2026

Singapore, Singapore

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Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, \citet{sakaue2024generalization} proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs, the optimal solutions of convex QPs are not confined to the vertices of the feasible polyhedron, and this complicates the analysis of the optimal value function. To overcome this challenge, we demonstrate that the solutions of convex QPs can be localized within a feasible region corresponding to a special active set, utilizing Carath\'{e}odory's theorem. Building on such observation, we propose the \textit{unrolled active set method}, which models the computation of the optimal value as a Goldberg-Jerrum (GJ) algorithm with bounded complexities, thereby establishing learning guarantees. We then further extend our analysis to the \textit{input-aware} setting , where we learn a mapping from QP problem instances to projection matrices.

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