MARLIN: Multi-Agent Reinforcement Learning for Incremental DAG Discovery

Causal discovery has shifted from data-centric methods to hybrid strategies that integrate semantic knowledge from experts or large language models (LLMs). Such external information is vital for identifying causal structures beyond the Markov Equivalence Class (MEC), which data alone cannot resolve. However, expert availability is often limited, and LLMs frequently misidentify causal directions in specialized domains. To overcome such shortcomings, we propose a tag-based approach that leverages semantically meaningful labels while deriving causal directionality directly from data. Using variable-level tag assignments from available sources (e.g., LLMs), our tags for DAGs method learns from identifiable data structures to extract higher-level causal relations. These are then used to orient undirected edges, enabling causal discovery to move beyond the MEC without reliance on fallible external knowledge.

Online reinforcement learning (RL) relies on the Markov property for guaranteed performance, but real-world applications often lack well-defined states given raw observed variables. While causal RL has attracted growing interest, existing work typically assumes Markovian states are provided and uses causality only to accelerate learning. This leaves a fundamental gap: given a longitudinal causal graph over observed variables, how does one construct MDP states that provably satisfy the Markov property? We provide a procedure that constructs a provably minimal such state. In deep RL, the minimal representation alone empirically fails to improve performance, indicating that neural networks cannot automatically exploit Markovian minimality. We therefore propose MOSE (Multi-Order State Exposure), which exposes a single shared Q-function to history-based state constructions of orders 1 through $W$ simultaneously. An attention-based selection layer scores the dimensions of this combined input by their estimated relevance to value-function estimation and selects the high-scoring ones. Causal MOSE further constrains the selection layer to retain every variable of the minimal state, guaranteeing sufficiency while leaving the model free to admit useful redundancy. MOSE consistently outperforms both the minimal state construction and single-window policies on common benchmarks and synthetic datasets. Including the minimal representation alongside MOSE can further improve performance. Our results establish a core principle for causal deep RL: minimal sufficiency is not enough. Controlled redundancy gives the model flexibility to learn its state representation end-to-end. Causal state information provides structural guidance that can make this learning more efficient.

Causal structure learning, also known as causal discovery, aims to estimate causal relationships between variables as a form of a causal directed acyclic graph (DAG) from observational data. One of the major frameworks is the order-based approach that first estimates a topological order of the underlying DAG and then prunes spurious edges from the fully-connected DAG induced by the estimated topological order. Previous studies often focus on the former ordering step because it can dramatically reduce the search space of DAGs. In practice, the latter pruning step is equally crucial for ensuring both computational efficiency and estimation accuracy. Most existing methods employ a pruning technique based on generalized additive models and hypothesis testing, commonly known as CAM-pruning. However, this approach can be a computational bottleneck as it requires repeatedly fitting additive models for all variables. Furthermore, it may harm estimation quality due to multiple testing. To address these issues, we introduce a new pruning method based on sparse additive models, which enables direct pruning of redundant edges without relying on hypothesis testing. We propose an efficient algorithm for learning sparse additive models by combining the randomized tree embedding technique with group-wise sparse regression. Experimental results on both synthetic and real datasets demonstrated that our method is significantly faster than existing pruning methods while maintaining comparable or superior accuracy.