Directed Perturbations for Efficient Learning of Surrogate Losses

Decision-Focused Learning (DFL) is a paradigm to learn neural network-based predictive models tailored to a specific optimisation problem. A key challenge for DFL methods lies in the non-differentiable nature of most optimisation problems. Recent solutions use a learned, differentiable, model to act as a surrogate loss. To learn the model, the optimisation problem is solved repeatedly using random perturbations of the predictions to calculate a regret value which can be used as a target to learn the surrogate loss. However, this necessitates numerous runs of the, potentially computationally expensive, optimiser. As such, maximising the useful information from each run of the optimizer is paramount. A sample of purely random perturbations may not yield an effective distribution to learning the surrogate from. We propose using a directed perturbation strategy to generate a set of meaningful perturbations for learning a surrogate loss model. We evaluate our approach on a resource allocation problem and real-world case study focused on a critical energy challenge: optimising solar-plus-battery systems. The results show that directed perturbations learn a stronger surrogate loss with fewer runs of the optimiser, enabling a more efficient DFL.