发表机构
University of Southern California; University of Michigan（南加州大学; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过雅可比秩刻画决策聚焦学习的更新限制，证明秩一雅可比导致梯度共线，实验显示DFL在多种任务中增益有限，仅背包问题在修正后有效，强调决策质量需实证检验。
AI 中文摘要
决策聚焦学习（DFL）通过下游目标训练预测器，但不同的损失未必提供独立的参数更新方向。我们通过预测器雅可比矩阵刻画这一限制，利用稀疏指数跟踪来区分优化器读取的协方差条目与学习可用的参数方向。秩为一的雅可比矩阵使非零的逐样本梯度共线；一个条件谱界描述了近共线情况。批量子空间刻画及反例表明，这些局部论断既不意味着共同的最小值点，也不意味着共线的批量更新。实验考察了几何性质何时转化为决策质量。在38种单参数权益配置中，DFL相对于MSE的增益保持在1.8%以下；一个385参数的条件下预测器也具有逐点秩一性。在验证调参的最短路径和背包实验中，全容量SPO+分别将平均遗憾降低了11.6%和10.6%；在八次比较中，只有背包在修正后仍然有效。容量对比在新鲜数据集上、跨批量顺序和训练预算下持续存在。在保持表达能力固定的情况下，可逆坐标缩放降低了谱有效秩和普通SGD的增益；补偿缩放则恢复了原始轨迹。金融前向目标控制将预测准确性与决策质量区分开来；匹配的神经比较在所测试架构中未发现DFL的总体优势。这些发现区分了局部秩限制、坐标依赖的优化和预测准确性。预测器几何有助于解释可用的学习方向，而留出的决策质量仍然是实际益处的检验标准。
英文摘要
Decision-focused learning (DFL) trains predictors through downstream objectives, but a different loss need not provide an independent parameter-update direction. We characterize this restriction through the predictor Jacobian, using sparse index tracking to distinguish the covariance entries read by the optimizer from the parameter directions available to learning. Rank-one Jacobians make nonzero per-example gradients collinear; a conditional spectral bound describes near-collinearity. A batch-subspace characterization and counterexamples show why these local statements imply neither common minimizers nor collinear batch updates. Experiments examine when geometry translates into decision quality. Across 38 one-parameter equity configurations, DFL gains over MSE remain below 1.8%; a 385-parameter conditional predictor also has pointwise rank one. In validation-tuned shortest-path and knapsack experiments, full-capacity SPO+ reduces mean regret by 11.6% and 10.6%, respectively; only knapsack survives correction across eight comparisons. The capacity contrast persists on fresh datasets across batch orders and training budgets. Holding expressivity fixed, invertible coordinate scaling lowers spectral effective rank and ordinary SGD gains; compensating for the scaling restores the original trajectories. Financial forward-target controls separate forecast accuracy from decision quality; a matched neural comparison finds no aggregate DFL advantage in the tested architecture. These findings distinguish local rank restrictions, coordinate-dependent optimization and predictive accuracy. Predictor geometry helps explain available learning directions, while held-out decision quality remains the test of practical benefit.
Comments53 pages, 21 figures, 32 tables. Includes theoretical proofs and supplementary experiments
