Solver-Free Decision-Focused Learning via Barrier Coordinate Cost Prediction

We present a novel, ultra fast, solver-free, highly effective method for decision-focused cost predictions based on log-barrier gradient transforms, and demonstrate its performance on a broad family of benchmarks. We learn an optimal decision policy for a log-smoothed LP via interior projection methods from constrained ML, and convert it to a decision-focused cost-prediction via a barrier gradient transform. We benchmarks against SPO+ on several large scale instances, and achieve lower regret and order of magnitude training speed-ups. Decision-focused learning (DFL) trains predictions for the quality of the decisions they induce, but leading methods repeatedly invoke an optimizer during training. We introduce "barrier cost recovery", a novel, ultra fast, solver-free, method for decision-focused learning, leveraging log-barrier gradient transforms, and demonstrate its performance on a broad family of benchmarks. A neural network learns an interior policy for a log-barrier-regularized problem through a fast feasibility chart. The negative barrier gradient then converts that policy into a decision-focused cost prediction. For every positive barrier weight, the method is Fishcer consistent. Additionally, the regret of the traning loss surrogate is exactly a barrier Bregman divergence. We add a closed-form prediction correction combines this decision coordinate with an MSE head to produce a physical-cost forecast without changing any decision. On the tested benchmarks, we achieve materially lower regret than SPO+ and MSE, and order of magnitude training speed-ups compared with SPO+