arXiv:2511.04909cs.LGcs.AI2025-11被引 2

用对偶变量指导训练,大幅减少优化器调用次数。

A Dual Perspective on Decision-Focused Learning: Scalable Training via Dual-Guided Surrogates

  • 通过下游问题的对偶变量构造可微代理损失,降低求解器依赖。
  • 训练成本趋近监督学习,但决策性能接近顶尖方法。
  • 适合需要高效训练组合优化决策模型的研究者。

许多现实决策需在不确定性下求解优化问题,依赖预测值。传统先预测后优化范式催生了决策感知学习(DFL),其通过考虑优化器如何使用预测值来提升下游决策性能。然而,现有方法要么需对求解器反向传播,要么依赖任务特定代理,均频繁调用昂贵的优化器(常为组合优化)。本文提出对偶引导损失(DGL),利用下游问题的对偶变量指导学习,构建一种简单且可扩展的目标函数。针对具有自然一一对应约束的组合选择问题(如匹配、背包、最短路径),本方法(a)通过周期性求解下游问题,将优化与梯度更新解耦;(b)在刷新之间,基于对偶调整的目标使用简单可微代理损失训练;(c)随着刷新频率降低,训练成本趋近标准监督学习,同时保持强决策一致性。我们证明了DGL具有渐近递减的决策遗憾,分析了运行时间复杂度,并在两类问题上验证:相比状态最优的DFL方法,DGL仅用极少求解器调用即达到或超越其性能,显著缩短训练时间。代码已公开于 https://github.com/paularodr/Dual-Guided-Learning。

原文摘要 · Abstract (English)

Many real-world decisions are made under uncertainty by solving optimization problems using predicted quantities. This predict-then-optimize paradigm has motivated decision-focused learning, which trains models with awareness of how the optimizer uses predictions, improving the performance of downstream decisions. Despite its promise, scaling is challenging: state-of-the-art methods either differentiate through a solver or rely on task-specific surrogates, both of which require frequent and expensive calls to an optimizer, often a combinatorial one. In this paper, we leverage dual variables from the downstream problem to shape learning and introduce Dual-Guided Loss (DGL), a simple, scalable objective that preserves decision alignment while reducing solver dependence. We construct DGL specifically for combinatorial selection problems with natural one-of-many constraints, such as matching, knapsack, and shortest path. Our approach (a) decouples optimization from gradient updates by solving the downstream problem only periodically; (b) between refreshes, trains on dual-adjusted targets using simple differentiable surrogate losses; and (c) as refreshes become less frequent, drives training cost toward standard supervised learning while retaining strong decision alignment. We prove that DGL has asymptotically diminishing decision regret, analyze runtime complexity, and show on two problem classes that DGL matches or exceeds state-of-the-art DFL methods while using far fewer solver calls and substantially less training time. Code is available at https://github.com/paularodr/Dual-Guided-Learning.

决策学习对偶优化组合优化可扩展性

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