DF2: Distribution-Free Decision-Focused Learning
Lingkai Kong Wenhao Mu Jiaming Cui Yuchen Zhuang B. Aditya Prakash Bo Dai Chao Zhang
Decision-focused learning (DFL) has recently emerged as a powerful approach
for predict-then-optimize problems by customizing a predictive model to a
downstream optimization task. However, existing end-to-end DFL methods are
hindered by three significant bottlenecks: model mismatch error, sample average
approximation error, and gradient approximation error. Model mismatch error
stems from the misalignment between the model's parameterized predictive
distribution and the true probability distribution. Sample average
approximation error arises when using finite samples to approximate the
expected optimization objective. Gradient approximation error occurs as DFL
relies on the KKT condition for exact gradient computation, while most methods
approximate the gradient for backpropagation in non-convex objectives. In this
paper, we present DF2 -- the first \textit{distribution-free} decision-focused
learning method explicitly designed to address these three bottlenecks. Rather
than depending on a task-specific forecaster that requires precise model
assumptions, our method directly learns the expected optimization function
during training. To efficiently learn the function in a data-driven manner, we
devise an attention-based model architecture inspired by the distribution-based
parameterization of the expected objective. Our method is, to the best of our
knowledge, the first to address all three bottlenecks within a single model. We
evaluate DF2 on a synthetic problem, a wind power bidding problem, and a
non-convex vaccine distribution problem, demonstrating the effectiveness of
DF2.