Prediction Loss Guided Decision-Focused Learning

Abstract: Decision-making under uncertainty is often considered in two stages: predicting the unknown parameters, and then optimizing decisions based on predictions. While traditional prediction-focused learning (PFL) treats these two stages separately, decision-focused learning (DFL) trains the predictive model by directly optimizing the decision quality in an end-to-end manner. However, despite using exact or well-approximated gradients, vanilla DFL often suffers from unstable convergence due to its flat-and-sharp loss landscapes. In contrast, PFL yields more stable optimization, but overlooks the downstream decision quality. To address this, we propose a simple yet effective approach: perturbing the decision loss gradient using the prediction loss gradient to construct an update direction. Our method requires no additional training and can be integrated with any DFL solvers. Using the sigmoid-like decaying parameter, we let the prediction loss gradient guide the decision loss gradient to train a predictive model that optimizes decision quality. Also, we provide a theoretical convergence guarantee to Pareto stationary point under mild assumptions. Empirically, we demonstrate our method across three stochastic optimization problems, showing promising results compared to other baselines. We validate that our approach achieves lower regret with more stable training, even in situations where either PFL or DFL struggles.