Competition is the key: A Game Theoretic Causal Discovery Approach

• URL: http://arxiv.org/abs/2510.20106v1
• Date: Thu, 23 Oct 2025 01:19:21 GMT
• Title: Competition is the key: A Game Theoretic Causal Discovery Approach
• Authors: Amartya Roy, Souvik Chakraborty,
• Abstract summary: We introduce a game-theoretic reinforcement learning framework for causal discovery.<n>A DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution.<n>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.
• Score: 2.248800010440909
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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. 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.

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