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

Computer Science > Artificial Intelligence [Submitted on 25 Mar 2026] Position Paper: Post-Solve Robustness in Decision Engines: Feasible Regions and Smoothness Under Perturbations Yi-Xiang Hu 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 \epsilon-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. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.00002 [cs.AI]   (or arXiv:2606.00002v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.00002 Focus to learn more Submission history From: Yi-Xiang Hu [view email] [v1] Wed, 25 Mar 2026 03:34:11 UTC (150 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)