GG-DFF: Geometry-Guided Decision-Focused Fine-Tuning

Decision-Focused Learning (DFL) trains predictive models for downstream optimization using decision quality as the learning signal. Existing methods make DFL tractable by differentiating through optimization layers, smoothing the optimizer with perturbations, or replacing the true decision loss with tractable surrogates. However, in linear and mixed-integer linear programs with linear objectives, the convex hull of feasible decisions induces a partition of the objective-parameter space into regions associated with different optimal decisions. The decision consequences of a prediction correction depend on the region it reaches, while equal reductions in surrogate loss can lead to decisions of different quality. To address this issue, we propose Geometry-Guided Decision-Focused Fine-Tuning (GG-DFF), which uses feasible-solution differences to guide prediction corrections. We compare the decision under the original prediction with collected feasible solutions. We then use the resulting difference vectors to construct a convex correction region (CCR) around the original prediction, which guides which decision regions prediction corrections can reach. Specifically, we freeze the pretrained predictor and learn corrections through an almost-everywhere differentiable parameterization of the CCR. This parameterization keeps corrected predictions inside the region and allows SPO+ gradients to propagate through its comparison geometry. Our theoretical analysis connects correction boundaries to decision-region reachability, establishes sufficient conditions for excluding decision regions, and derives conditional regret bounds relative to the pretrained decision. Experimental results show that GG-DFF reduces mean normalized decision regret relative to the reference fine-tuning baseline by up to 17.7%, 1.0%, 2.9%, and 2.2% on shortest path, knapsack, Energy-1, and Energy-2, respectively.