# Competition is the key: A Game Theoretic Causal Discovery Approach

arXiv: https://arxiv.org/abs/2510.20106 · HTML: https://mlsanity.com/paper/2510.20106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)
- [On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimization](https://mlsanity.com/paper/2106.02835/) (2021)

## Abstract (arXiv)

Causal discovery remains a central challenge in machine learning, yet existing methods face a fundamental gap: algorithms like GES and GraN-DAG achieve strong empirical performance but lack finite-sample guarantees, while theoretically principled approaches fail to scale. We close this gap by introducing a game-theoretic reinforcement learning framework for causal discovery, where a DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution. This design yields three provable guarantees: the learned graph is never worse than the opponent, warm-starting strictly accelerates convergence, and most importantly, with high probability the algorithm selects the true best candidate graph. To the best of our knowledge, our result makes a first-of-its-kind progress in explaining such finite-sample guarantees in causal discovery: on synthetic SEMs (30 nodes), the observed error probability decays with n, tightly matching theory. On real-world benchmarks including Sachs, Asia, Alarm, Child, Hepar2, Dream, and Andes, our method consistently improves upon GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 (70 nodes), Dream (100 nodes), and Andes (220 nodes). Together, these results establish a new class of RL-based causal discovery algorithms that are simultaneously provably consistent, sample-efficient, and practically scalable, marking a decisive step toward unifying empirical performance with rigorous finite-sample theory.