Counterfactual Optimal Action Trees (COAT): Interpretable Prescriptive Policies from Observational Data

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

Explainable artificial intelligence (XAI) increasingly calls for actionable counterfactual recourse, yet current methodologies face challenges related to causal invalidity, excessive cognitive burden, and predictive failure. Exhaustive causal search algorithms often require modifications to multiple attributes, whereas additive attribution-guided methods, such as SHAP, ignore higher-order feature synergies, leading to suboptimal predictive momentum and diffuse intervention effort in complex nonlinear models, such as XGBoost. To bridge this gap, we introduce actionable case-based feature importance (A-CBFI), a diagnosis-prescription integrated framework for tabular machine learning. Grounded in structural causal models (SCMs), A-CBFI isolates synergistic interaction bottlenecks and releases suppressive structural locks, translating them into targeted interventions. By mathematically separating the active user intervention space (L_{\mathrm{active}}) from downstream effects and concentrating over 98.3% of the intervention effort on diagnosed root causes, A-CBFI enables highly targeted interventions. Empirical evaluations across the financial and healthcare domains demonstrate that A-CBFI reduces the active human intervention burden by 77.0% while maintaining comparable global recourse cost to exhaustive causal baselines. By prioritizing the diagnosed causal bottlenecks, A-CBFI provides targeted and actionable recourse while maintaining causal validity and achieving full relative convergence across all causally feasible instances.

We introduce a causal aware foundation-model framework for real time optimal decision making in discrete choice environments. We propose a constrained triple-head price optimization (C3PO) network to solve a bilevel decision problem in which a service provider selects an optimal assortment while heterogeneous users make personalized acceptance or rejection choices optimizing their own personalized preferences. C3PO integrates imitation learning of prices, multi-task learning of revenue responses, and in context learning of price elasticity to generate pricing recommendations while adhering to business constraints. During inference, frontier model prompting retrieves an enhanced elasticity prior for new products from behavioral economics literature, improving pricing effectiveness. We demonstrate strong in context learning performance using simulated, synthetic, and real-world datasets. C3PO is trained on simulated data generated from multiple classical discrete choice models in economics. The model is trained on data comprising simulated customer segments and counterfactual action and outcome pairs and evaluated on randomly generated choice environments with no access to the underlying preference structure. The trained model consistently improves the pricing KPIs, with gains increasing as customer price sensitivity increases. We also deploy the tuned foundation model for optimal pricing in real-world applications such as healthcare, tender pricing, airline ancillary pricing, and other domains, achieving substantial gains across multiple products, markets, and divisions.