Causal Discovery with Reinforcement Learning (1906.04477v4)

Abstract: Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are usually less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows a flexible score function under the acyclicity constraint.

• The paper introduces a novel RL-driven approach that uses an encoder-decoder model and penalty framework to efficiently learn causal DAG structures.
• Experimental results show that RL-BIC2 outperforms methods like NOTEARS and DAG-GNN, achieving high accuracy and zero false discovery rates on synthetic benchmarks.
• The approach offers a flexible framework that integrates traditional scoring functions with innovative acyclicity constraints to overcome sample size limitations in causal discovery.

An Expert Review of "Causal Discovery with Reinforcement Learning"

The paper "Causal Discovery with Reinforcement Learning" by Shengyu Zhu, Ignavier Ng, and Zhitang Chen presents an innovative approach to identifying causal structures within a set of observable variables. Traditional methods in this area rely heavily on score-based techniques and local heuristics to determine a Directed Acyclic Graph (DAG) that best fits the data according to some predefined scoring function. These methods, while theoretically sound under ideal conditions, often struggle in practical applications characterized by limited sample sizes and violations of underlying assumptions.

The authors propose a solution leveraging the capabilities of Reinforcement Learning (RL) to enhance the search for optimal DAGs. Unlike standard RL applications focused on learning policies, this work uses RL primarily as a search mechanism. The focus is on generating the graph that optimizes reward signals, incorporating both the scoring function and an innovative penalty framework to enforce acyclicity—key to maintaining valid causal relationships.

Methodology

The crux of the proposed method involves an encoder-decoder neural network model. The encoder processes the observable data to capture variable interactions, while a novel decoder iteratively constructs adjacency matrices representing potential causal links. The RL framework assesses the constructed graphs using a reward function that balances the scoring function and penalties for acyclic violations.

The authors conduct experiments on both synthetic and real-world datasets to evaluate their method. The results demonstrate that this approach significantly enhances the search capability for causal discovery while maintaining the flexibility to utilize various scoring functions constrained by acyclicity. On synthetic datasets, their model, RL-BIC2, particularly excelled in identifying the true causal graphs, outperforming other modern approaches like NOTEARS and DAG-GNN, especially in cases with nonlinear causal relationships.

Results and Implications

The experiments highlight the proposed method’s robustness in recovering underlying causal structures even in nonlinear scenarios. The authors detail strong empirical performance metrics, such as zero false discovery rates on certain datasets, underscoring the accuracy of their approach. Moreover, RL-BIC2 demonstrates significant improvement over Greedy Equivalence Search (GES) when using the same Bayesian Information Criterion (BIC), showcasing the enhanced search capability provided by the RL paradigm.

Theoretically, utilizing RL as a search strategy introduces a robust way to dynamically explore the space of possible DAGs, driven by reward-guided exploration and exploitation dynamics intrinsic to RL. Practically, this paper’s framework allows for seamless incorporation of both traditional and novel scoring functions, broadening the applicability of causal discovery across diverse scientific domains.

Future Directions

The paper opens avenues for further research in large-scale causal discovery tasks. While their approach shows competitiveness with graphs of up to 30 nodes, real-world applications often exceed this scale. Future works may focus on refining the RL model to accommodate larger datasets and incorporate scalable frameworks that partition causal discovery tasks.

In concluding, the paper effectively argues for the role of RL in causal discovery, overcoming limitations tied to sample size and assumption violations in traditional methods, and setting a new benchmark for flexible, robust causal analysis. As RL evolves, its intersection with causal discovery offers promising prospects for deeper scientific insights across empirical sciences.