DF2: Distribution-Free Decision-Focused Learning

TL;DR

DF2 introduces a distribution-free decision-focused learning approach that directly learns the expected optimization function, effectively addressing model mismatch, sampling, and gradient errors without relying on task-specific forecasters.

Contribution

It is the first method to mitigate key bottlenecks in probabilistic decision-focused learning by directly learning the expected objective in a distribution-free manner.

Findings

DF2 outperforms existing methods on synthetic problems.

DF2 demonstrates effectiveness on real-world problems.

The approach reduces errors associated with model mismatch and sampling.

Abstract

Decision-focused learning (DFL), which differentiates through the KKT conditions, has recently emerged as a powerful approach for predict-then-optimize problems. However, under probabilistic settings, DFL faces three major 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 when the objectives are non-convex and KKT conditions cannot be directly applied. In this paper, we present DF2, the first distribution-free decision-focused learning method designed to mitigate 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 this function in a data-driven manner, we devise an attention-based model architecture inspired by the distribution-based parameterization of the expected objective. We evaluate DF2 on two synthetic problems and three real-world problems, demonstrating the effectiveness of DF2. Our code is available at: https://github.com/Lingkai-Kong/DF2.