Decision-Focused Learning via Tangent-Space Projection of Prediction Error
For practitioners of decision-focused learning, this provides a computationally efficient and theoretically grounded alternative to existing regret gradient methods, improving both decision quality and training speed.
The paper proposes PEAR, a method that computes regret gradients for Decision-Focused Learning by projecting prediction error onto the tangent space of active constraints, avoiding expensive differentiation through solvers. Experiments show PEAR achieves the best decision quality among baselines while being the most computationally efficient, with gains persisting under constraint shifts.
Decision-Focused Learning (DFL) trains predictors to improve downstream decision quality, but computing regret gradients typically requires differentiating through solvers or relying on surrogate losses, which can be computationally expensive or deviate from the true objective. We show that, under standard regularity with locally stable active constraints, the regret gradient admits a closed-form geometric characterization, equivalent to the prediction error projected onto the tangent space of active constraints, scaled by local curvature. This reveals that regret gradients can be obtained by filtering decision-irrelevant components from the MSE gradient, providing a simpler and more direct alternative to existing approaches. Based on this, we propose PEAR (Projected Error As Regret-gradient), which computes regret gradients via a reduced linear system over active constraints, avoiding differentiation through solver iterations or additional optimization solves. Experiments on LP benchmarks and a real-world QP task show that PEAR achieves the best decision quality among all baselines while being the most computationally efficient, with gains that persist under constraint shifts.