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CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery

🕒 Published (v1): 2026-07-02 09:29 UTC · Source: Arxiv · link

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Agentic divide-conquer-combine for causal discovery; practical copilot pattern

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TL;DR

CausalSteward (CaST) is a multi-agent, human-in-the-loop copilot for causal discovery that applies a divide-and-conquer strategy to high-dimensional variable sets, fusing LLM prior knowledge, retrieval-augmented generation (RAG), and constraint-based statistical algorithms. By recursively partitioning variables into causally coherent clusters and estimating local causal graphs that are subsequently merged, CaST scales to dataset sizes where monolithic LLM or classical approaches are intractable. Ablations confirm that HITL and RAG are jointly necessary for peak performance.

Problem

Causal discovery from observational data faces two compounding challenges: (1) causal identifiability failures when core assumptions (e.g., causal sufficiency, linearity) are violated, and (2) exponential scaling of classical constraint-based methods (e.g., FCI) with variable count, making them computationally prohibitive in high-dimensional settings. LLM-based approaches are bounded by finite context windows and produce unwieldy edge-lists at scale, while purely manual expert annotation is infeasible. No existing framework interactively integrates LLM prior knowledge, RAG, real domain expert feedback, and data-driven discovery in a scalable architecture.

Method

CaST operates in four sequential phases executed by specialized LLM agents:

  1. Explain: An Explainer agent \(\mathcal{E}\) ingests variable labels and a user-provided dataset description, producing enriched per-variable descriptions \(I = \mathcal{E}(X_\text{labels}, p_\text{explain})\) to reduce ambiguity.

  2. Divide: A hypothesis agent \(D_\text{hyp}\) proposes a causal partitioning \(\{P_{i,1},\ldots,P_{i,N}\} = D_\text{hyp}(P_i, p_\text{div.hyp})\) and a critic agent \(D_\text{critic}\) refines it. Partitioning recurses until each leaf partition has \(\leq k\) variables, forming a causal partition tree grounded in Definition 3 (Causal Partitioning).

  3. Conquer: For each leaf partition \(P_i\), a hypothesis agent generates a causal graph \(G^i_\text{hyp}\), a critic refines it to \(G^i_\text{critic}\), and then FCI (or ICD) is bootstrapped with \(G^i_\text{critic}\) as edge constraints to produce the data-driven local PAG \(\tilde{G}^i_\text{critic} = F(D_i, G^i_\text{critic})\).

  4. Combine: Merge-hypothesis and merge-critic agents traverse the partition tree bottom-up, proposing and refining inter-partition edges to assemble the global causal graph.

Throughout all phases, agents invoke RAG (web search) and HITL tool calls on-demand to retrieve external causal knowledge or resolve uncertainties with domain experts.

Theoretical guarantees: Under an ideal causal partitioning and large-sample limit, CaST inherits FCI's asymptotic consistency (Theorem 1). For non-ideal partitions, expected total SHD is bounded as: $\(\mathbb{E}[\text{SHD}_\text{total}] \approx (S_A + N_\text{NotIntra} \cdot FPRC) + (E_\text{cut}(1-\text{Rec}_M) + m \cdot FDR_M)\)$ where \(S_A\) = spurious adjacencies, \(FPRC\) = conquer false-positive rate, \(\text{Rec}_M\) = merge recall, \(FDR_M\) = merge false-discovery rate.

Key Contributions

  • First interactive multi-agent framework applying a divide-and-conquer paradigm to high-dimensional causal discovery.
  • Four-phase architecture (Explain → Divide → Conquer → Combine) with hypothesis/critic agent pairs at each structural step.
  • On-demand HITL and agentic RAG tool calls integrated into every agent, enabling dynamic knowledge retrieval.
  • Formal consistency theorem (Theorem 1) under ideal causal partitioning; error decomposition theorem (Theorem 2) for non-ideal cases.
  • Empirical evaluation across manufacturing (CausalMan), neuropathic pain, and CausalChambers datasets against seven baselines, with real domain-expert HITL on CausalMan.

Results

All numbers from Table 1 (CausalMan Small/Medium, F1 / Precision / SHD, mean ± std over 5 seeds):

  • CausalMan Small: CaST (HITL+RAG) with o4-mini achieves F1 = 0.424, Precision = 0.724, SHD = 103.0; CaST (HITL) reaches F1 = 0.483, Precision = 0.608, SHD = 102.4 — outperforming best non-CaST baseline LLM-BFS (F1 = 0.283, Precision = 1.000, SHD = 315.2) on F1 and SHD by large margins.
  • CausalMan Medium: FCI, LLM-BFS, and LLM-Pairwise are intractable; CaST (RAG) achieves F1 = 0.211 vs. CausalCopilot's F1 = 0.057, demonstrating scalability.
  • CS (flat conquer, no divide) generally underperforms CaST on Small but is competitive on Medium, indicating the divide phase adds most value at finer granularity.
  • Ablation: RAG-only variant consistently lower F1 than HITL variants, confirming both components are necessary for peak performance.
  • CaST tested with GPT-4o-mini, o3-mini, and Qwen3-14B; o4-mini/o3-mini variants show strongest results.

Limitations

  • HITL experiments require real domain experts, making evaluation expensive and difficult to scale; neuropathic pain HITL used simulated experts.
  • The divide phase relies on LLM heuristics for causal partitioning, which is theoretically intractable; incorrect partitions degrade performance per Theorem 2.
  • Performance drops substantially from Small to Medium datasets (F1 ~0.42 → ~0.27 for best CaST variant), suggesting scalability gains are partial.
  • Context-window constraints of LLMs still limit the maximum partition size \(k\) and the depth of the partition tree.
  • No evaluation on fully synthetic ground-truth graphs with known identifiability properties beyond CausalChambers.
  • RAG web search quality is not controlled and may introduce noise or hallucinated causal claims.

Relevance to Agentic AI / LLM Agents

CaST is a concrete instantiation of multi-agent collaboration with structured tool use (RAG, HITL calls, statistical algorithms), directly advancing the paradigm of agents as scientific copilots rather than end-to-end solvers. The hypothesis/critic agent pair pattern — where one agent proposes and another adversarially refines — is a reusable agentic design primitive applicable beyond causality. The framework also explicitly probes the limits of LLM causal reasoning in multi-agent settings, providing one of the first empirical analyses of how agent-count, divide granularity, and knowledge-retrieval mode jointly govern accuracy on a structured reasoning task. For the broader agentic-AI community, the theoretical error decomposition (Theorem 2) offers a rare formal tool for analyzing how component-level agent failures compound in a pipeline architecture.