Title: Competition is the key: A Game Theoretic Causal Discovery Approach
Primary area: causal reasoning
Keywords: Causal Discovery, Reinforcement Learning

Abstract: 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. Formally, if the sample size $n$ is sufficiently large, specifically 
$
n \geq \tfrac{8L^2}{\Delta_n^2}\log\biggl(\tfrac{2|C|}{\delta}\biggr),
$
then with probability at least $1-\delta$ our method recovers the population-optimal graph. Here $L$ is a Lipschitz constant of the score function, $\Delta_n$ is the empirical gap between the best and second-best candidate scores, $|C|$ is the number of candidate graphs considered, and $ \forall\delta \in (0,1)$ is the failure probability . Thus, to the best of our knowledge, our result here makes a first-of-its-kind progress with 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, Dream4, and Andes, our method consistently outperforms GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 ($\sim$70 nodes), Dream4 ($\sim$100 nodes), and Andes ($\sim$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.