Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities

TL;DR

This paper provides a comprehensive review of decision-focused learning (DFL), an end-to-end paradigm that trains ML models within constrained optimization to improve prescriptive decisions under uncertainty. It distinguishes gradient-based and gradient-free DFL approaches, offering a four-class taxonomy for gradient-based methods and extensive discussion of surrogate losses, smoothing, and black-box differentiation strategies. The authors benchmark eleven DFL methods across seven problems, providing empirical insights into when different techniques excel and highlighting trade-offs in computation, accuracy, and scalability. They also outline future directions, including extending DFL to non-linear, robust, multistage, and multimodal settings, aiming to broaden its practical impact in real-world decision making.

Abstract

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Figures (21)

• Figure 1: Decision-making under uncertainty involves both predictive and prescriptive analytics. In the predictive stage, the uncertain parameters are predicted from the features using an ML model. In the prescriptive stage, a decision is prescribed by solving a CO problem using the predicted parameters.
• Figure 2: An illustrative numerical example with a knapsack problem with two items to exemplify the discrepancy between prediction error and regret. The figure illustrates that two points can have the same prediction error but different regret. Furthermore, it demonstrates that overestimating the values of the selected items or underestimating the values of the items that are left out does not change the solution, and thus does not increase the regret, even though the prediction error does increase.
• Figure 3: In decision-focused learning, the neural network model is trained to minimize the task loss
• Figure 4: An overview of gradient-based DFL methodologies categorized into four classes.
• Figure 5: Comparative evaluations on the synthetic shortest path problem with noise-halfwidth parameter $\vartheta$ = 0.5. The boxplots show the distributions of relative regrets.