Decision-Focused Learning: Learning to Rank Based on Sample Average Approximation

Qi Zhang, Yunxia Wu, Yangsheng Jiang, Lishengsa Yue, Zhihong Yao

Keywords: Decision-Focused Learning, Learning to Rank, Sample Average Approximate, Ranking subset construction

Abstract: Decision-Focused Learning (DFL) improves prediction models by directly optimizing the decision quality of downstream optimization problems, where Learning to Rank (LTR) approaches treat the solution set as a ranking set and design surrogate losses based on the objective function. The DFL-LTR framework exhibits strong applicability; however, it lacks a specially designed subset construction method, which limits its performance. To address this issue, tailored to the intrinsic characteristics of the DFL-LTR framework, we first articulate two fundamental bottlenecks that any ranking subset construction must resolve: ($i$) the infeasibility of fully enumerating the solution space; ($ii$) the resulting upper bound on the loss function family that remains unbroken. To eliminate these limitations, we introduce a ranking subset construction paradigm driven by Sample Average Approximation (SAA). By performing stochastic optimization over minibatches, the proposed method yields an equivalent approximation of the complete solution set, suppresses loss variance to stabilise gradients, and consequently elevates the performance upper bound of the entire framework. Our LTR-SAA subset construction module is fully plug-and-play: it introduces no extra hyperparameters, incurs zero additional time complexity, and remains compatible with the entire family of LTR loss functions. In the latest open-source benchmark (comprising 7 optimization problems), our proposed method achieves SOTA decision quality on 5 of these problems. Compared with other DFL and 2-stage methods, it demonstrates significant performance advantages and generality. Code is available at https://anonymous.4open.science/r/SAA-LTR-33B0.

Primary Area: optimization

Submission Number: 5948