选出关键不确定方向，让模型更鲁棒且计算高效。
Which Directions Matter? Sparse Design for Affine Robust Optimization
- 从有限方向中筛选关键不确定方向，构建可计算的鲁棒优化模型。
- 提出数据驱动选择规则，在评估方向上覆盖度达最优，逼近率93%。
- 适合关注模型鲁棒性与计算效率的研究者，尤其适用于对抗训练场景。
鲁棒机器学习与优化依赖于不确定性建模。本文研究在有限词典和预算约束下，模型需覆盖哪些不确定性方向。通过选取子集构成原子不确定性集，其支撑函数具闭式表达，使仿射目标的鲁棒规划可求解。提出基于评估方向（如梯度、对抗扰动或保留数据上的偏移）的覆盖目标的数据驱动选择规则。证明该目标单调且子模，支持贪心算法，具有(1−1/e)近似保证，并存在紧致困难界。还提供所选子集损失的上界证书及样本外控制的半径校准规则。
原文摘要 · Abstract (English)
Robust machine learning and optimization rely on the uncertainty model choice. We investigate which uncertainty directions a model must cover when defined by a finite dictionary and a budget constraint. Selecting a subset forms an atomic uncertainty set with a closed form support function, yielding tractable robust programs for affine objectives. We propose a data driven selection rule based on a coverage objective over evaluation directions, including gradients, adversarial perturbations, or shifts observed on held out data. We prove this objective is monotone and submodular, supporting a greedy method with a $(1-1/e)$ approximation guarantee and a matching hardness barrier. We also provide a certificate bounding the loss from the selected subset and a radius calibration rule with out of sample control.
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