Robust Losses for Decision-Focused Learning
Noah Schutte Krzysztof Postek Neil Yorke-Smith
Optimization models used to make discrete decisions often contain uncertain
parameters that are context-dependent and are estimated through prediction. To
account for the quality of the decision made based on the prediction,
decision-focused learning (end-to-end predict-then-optimize) aims at training
the predictive model to minimize regret, i.e., the loss incurred by making a
suboptimal decision. Despite the challenge of this loss function being possibly
non-convex and in general non-differentiable, effective gradient-based learning
approaches have been proposed to minimize the expected loss, using the
empirical loss as a surrogate. However, empirical regret can be an ineffective
surrogate because the uncertainty in the optimization model makes the empirical
regret unequal to the expected regret in expectation. To illustrate the impact
of this inequality, we evaluate the effect of aleatoric and epistemic
uncertainty on the accuracy of empirical regret as a surrogate. Next, we
propose three robust loss functions that more closely approximate expected
regret. Experimental results show that training two state-of-the-art
decision-focused learning approaches using robust regret losses improves
test-sample empirical regret in general while keeping computational time
equivalent relative to the number of training epochs.