# Decision-Focused Learning in Network Interdiction Games

arXiv: https://arxiv.org/abs/2608.09036 · HTML: https://mlsanity.com/paper/2608.09036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Behavioral and Game-Theoretic Security Investments in Interdependent Systems Modeled by Attack Graphs](https://mlsanity.com/paper/2001.03213/) (2020)

## Abstract (arXiv)

We study decision-focused learning (DFL) in shortest-path network interdiction (SPNI) games, a Stackelberg game where an interdictor (leader) strengthens the networks' arcs against attacks, while an evader (follower) who is uncertain about costs of attacking network arcs relies on a machine-learned predictor to identify the shortest path. While DFL is highly effective as an end-to-end optimization framework, we show that it faces a fundamental structural failure when employed in this game setting: its training objective admits a broad decision-equivalence class of cost estimators that achieve zero nominal loss yet fail under interdiction, reversing DFL's usual advantage over a naive prediction-focused learning (PFL) approach. To address this, we propose Adversarial DFL (A-DFL), which replaces nominal training samples with interdicted scenarios to collapse the harmful equivalence class. Experiments on synthetic and real-world networks confirm that A-DFL restores DFL's advantage in this game setting, enabling effective end-to-end optimization.