Constraint-Anchored Attribution: Feasibility-Certified Counterfactuals and Bonferroni-PAC Sufficient Subsets for Neural CO Policies

2026-05-24

AI Summary

This work addresses the lack of feasibility guarantees and statistical rigor in existing attribution methods for neural combinatorial optimization (CO). It proposes the first verifiable explanation framework that integrates constraint-anchored attribution, combinatorial feasibility certification, and Bonferroni-PAC statistical guarantees. The approach decomposes decisions by constraint families using LP relaxation duality, certifies counterfactual feasibility via a constraint satisfaction problem (CSP) model, and constructs PAC-sufficient subsets under greedy ordering through Bonferroni-corrected Hoeffding tests to control explanation size. Experiments demonstrate attribution accuracies of 96.5% and 77.2% on CVRPTW and Orienteering problems, substantially outperforming gradient-based surrogates; in FJSP tasks, all CSP-certified flips are consistent, with high-fidelity explanations generated using only 5.0 nodes on average.

Abstract

We give an attribution method for neural combinatorial-optimisation (CO) policies that (i) decomposes a decision by constraint families via LP-relaxation duals, (ii) certifies counterfactuals through a combinatorial feasibility model (implemented as a CSP feasibility-decision model), and (iii) bounds the size of a PAC-sufficient explanation with a Bonferroni-corrected Hoeffding sufficient-subset test along a greedy ordering. Across three CO problems and three seeds, our LP-anchored $Λ$-attribution matches the CF-derived signal at 96.5% on CVRPTW (n_cert=344) and 77.2% on the Orienteering Problem (n_cert=281) vs 75.0% and 35.2% for proxy gradient (paired diffs +0.215 and +0.420; McNemar exact $p \le 10^{-14}$). In the rank-aligned regime of the Flexible Job-Shop Scheduling Problem, both backends agree on every CSP-certified flip (n_cert=59), confirming the no-gain prediction. Bonferroni-PAC subsets average 5.0 nodes per step ($M=70$, $\varepsilon=δ=0.2$, $k_{\max}=25$). Reference implementation: https://github.com/sohaibafifi/neuro-co-cax

Problem

• attribution
• combinatorial optimization
• counterfactuals
• feasibility certification
• PAC explanation

Innovation

• Constraint-Anchored Attribution
• Feasibility-Certified Counterfactuals
• Bonferroni-PAC Sufficient Subsets
• Neural Combinatorial Optimization
• LP-Relaxation Duals