arXiv:2606.00002cs.AI2026-06

为优化决策系统提供部署后鲁棒性评估,验证解在扰动下的可信范围。

Position Paper: Post-Solve Robustness in Decision Engines: Feasible Regions and Smoothness Under Perturbations

  • 定义参数空间中ε近优可行邻域与决策空间平滑性,量化解的鲁棒边界。
  • 提出可认证的解周围内逼近、概率鲁棒性估计与对抗鲁棒性边界。
  • 适合高风险工业决策系统开发者,用于评估解在实际部署中的稳定性。

混合整数线性规划(MILP)决策引擎常输出高风险工业系统中看似最优的方案。然而,部署时很少满足求解时的假设:成本、需求或资源可用性的微小扰动可能导致可行性失效或引发解的质变。本文指出,当前优化流程缺失了部署后的鲁棒性评估维度,尤其对学习型决策系统而言。我们提出一个后求解鲁棒性层,不替代鲁棒优化或随机规划,而是审计已求得的解,提供基于求解器证据的可信范围。我们形式化两个核心对象:(i) 参数空间中ε-近优可行邻域,刻画解在扰动下保持可行且近优的范围;(ii) 决策空间中的解平滑性,衡量通过小组合变动得到的近似解是否仍具竞争力。整合灵敏度分析、稳定性理论、邻域搜索、对抗测试与学习增强技术,构建统一后求解鲁棒性框架。具体建议包括:解周围的可认证内逼近、校准不确定性的概率鲁棒性估计、对抗鲁棒性裕度,以及与求解器验证对齐的学习预测与解释。最后提出简洁报告模板与评估协议,使鲁棒性成为决策引擎的首类输出。

原文摘要 · Abstract (English)

Mixed-Integer Linear Programming (MILP) decision engines routinely output nominally optimal plans for high-stakes industrial systems. Yet deployment rarely matches solve-time assumptions: small perturbations in costs, demands, or resource availability can invalidate feasibility or trigger discontinuous shifts to qualitatively different solutions. We argue that this post-solve robustness gap is a missing layer in today's optimization pipelines and a missing evaluation dimension for learning-enabled decision systems. Rather than replacing robust optimization or stochastic programming, the proposed layer audits a solved incumbent and returns solver-backed evidence about how far that solution can be trusted. We formalize two central objects: (i) an $ε$-near-optimal feasible neighborhood in parameter space, capturing when an incumbent remains feasible and near-optimal under perturbations, and (ii) solution smoothness in decision space, capturing whether nearby alternatives with small combinatorial edits remain competitive. We then synthesize the most relevant partial answers from sensitivity and stability analysis, robust optimization, neighborhood search, adversarial testing, and learning-based enhancements, and articulate an agenda for a unified post-solve robustness layer. Concretely, we call for certified inner approximations around the incumbent, probabilistic robustness estimation with calibrated uncertainty, adversarial robustness margins, and learning-based prediction and explanation aligned with solver-backed verification. We conclude with a compact reporting template and evaluation protocol that would make robustness a first-class output of decision engines.

优化鲁棒性MILP决策系统后求解分析

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