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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Divide-conquer-combine agentic pattern for causal discovery; reusable scaffold design

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TL;DR

CausalSteward (CaST) is a multi-agent, human-in-the-loop copilot for causal discovery in high-dimensional data. It decomposes the variable set into causally coherent clusters via an iterative Divide phase, estimates local PAGs per cluster in a Conquer phase, then merges them in a Combine phase—augmenting each step with RAG and on-demand human queries. The framework proves asymptotic consistency under ideal partitioning and shows strong empirical gains over seven LLM- and data-driven baselines.

Problem

Constraint-based causal discovery (e.g., FCI, ICD) scales exponentially in the number of variables because the number of candidate conditioning sets grows combinatorially, making it intractable for high-dimensional data. LLMs alone fail in this regime because large edge-lists overflow context windows and LLM causal reasoning suffers from memorization and poor generalization. Manual expert specification of edge constraints is similarly unfeasible at scale, and integrating unstructured prior knowledge (text corpora, domain documents) into the discovery pipeline remains an open problem.

Method

CaST orchestrates four phases using specialized LLM agents, with RAG and human interaction available as tool calls to every agent:

1. Explain: An Explainer agent \(E\) expands dataset metadata into rich per-variable descriptions \(I = E(X_\text{labels}, p_\text{explain})\), disambiguating variable semantics before any discovery.

2. Divide: A Divide-hypothesis agent \(D_\text{hyp}\) proposes a causal partitioning \(\{P_{i,1},\ldots,P_{i,N}\} = D_\text{hyp}(P_i, p_\text{div.hyp})\) (partitions may initially overlap); a Divide-critic agent \(D_\text{critic}\) reviews and corrects it. The process recurses on any partition with more than \(k\) variables, building a partition tree until leaf clusters are granular enough for local causal discovery.

3. Conquer: For each leaf partition \(P_i\), a Hypothesis agent proposes an initial causal graph \(G_i^\text{hyp}\); a Critic agent refines it to \(G_i^\text{critic}\). A constraint-based algorithm (FCI) is then bootstrapped with \(G_i^\text{critic}\) as edge constraints: \(\tilde{G}_i^\text{critic} = F(D_i, G_i^\text{critic})\), blending LLM priors with data-driven conditional independence tests.

4. Combine: Merge-hypothesis and Merge-critic agents propose and refine inter-partition edges following the partition tree bottom-up: $\(G_\text{comb}^\text{hyp} = M_\text{hyp}(G_1,\ldots,G_M, p_\text{comb}), \quad G_\text{comb}^\text{critic} = M_\text{critic}(G_\text{comb}^\text{hyp}, p_\text{comb}).\)$

RAG: An agentic web-search RAG system is summoned on-demand via tool call. HITL: Agents issue targeted clarification queries to the human expert when uncertain, rather than requiring exhaustive upfront constraint specification.

Key Contributions

• First interactive multi-agent Divide-and-Conquer framework for causal discovery, capable of handling high-dimensional settings where prior methods are intractable.
• Theorem 1 (Consistency): If \(D_\text{hyp}/D_\text{critic}\) yield a valid causal partitioning (Def. 3) and FCI is run consistently, the union of local PAGs is a consistent global PAG.
• Theorem 2 (SHD decomposition): \(\mathbb{E}[\text{SHD}_\text{total}] \approx (SA + N_\text{NotIntra} \cdot FPRC) + (E_\text{cut}(1-\text{Rec}_M) + m \cdot FDR_M)\), quantifying error contributions from partitioning errors, conquer false positives, and merge recall/FDR.
• Hypothesis-Critic agent pairs at both Divide and Combine phases, providing a built-in self-correction mechanism.
• Ablation study isolating RAG, HITL, and their combination, showing both are jointly necessary for peak performance.

Results

All results on CausalMan benchmark (Small and Medium splits); metrics: F1, Precision, SHD (lower is better for SHD). Five seeds, mean ± std reported.

• CausalMan Small — Best CaST variant (o3-mini, HITL): F1 = 0.483, Prec = 0.608, SHD = 102.4; best baseline LLM-BFS (o3-mini): F1 = 0.283, SHD = 315.2 — CaST ~71% relative F1 improvement.
• CausalMan Small — CaST (o3-mini, HITL+RAG): F1 = 0.424, Prec = 0.724, SHD = 103.0 vs. CausalCopilot (best non-LLM-BFS baseline): F1 = 0.078, SHD = 221.4.
• CausalMan Medium — FCI, LLM-BFS, and LLM-Pairwise are intractable; GranDAG: F1 = 0.014; CaST (o3-mini, HITL+RAG): F1 = 0.274, Prec = 0.656, SHD = 558.0.
• Ablation: RAG-only consistently underperforms HITL-only and HITL+RAG, confirming that human domain knowledge is not replaceable by web retrieval alone on specialized datasets.
• Weaker LLMs (Qwen3-14B, o4-mini) yield meaningfully lower performance, showing results are LLM-capability-sensitive.

Limitations

• Partitioning accuracy is a hard ceiling: Theorem 2 shows SHD grows linearly with inter-partition edge cuts missed by Divide agents; no recovery mechanism fully compensates.
• HITL requires real domain experts during inference, which is costly and not always available; experiments relied on manufacturing domain experts for CausalMan.
• LLM causal reasoning limitations (memorization, failure to generalize) directly contaminate hypothesis quality in the Conquer phase.
• Overlapping initial partitions from \(D_\text{hyp}\) require correction by \(D_\text{critic}\), but correctness of the critic is not formally guaranteed.
• Results on the Neuropathic-Pain dataset and full ablation tables are in appendices not included in the provided excerpt.

Relevance to Harnesses / Meta-Harnesses

CaST is a canonical example of a multi-agent harness structured as a deterministic pipeline: specialized agents (Explainer, Divider, Critic, Conqueror, Combiner) are composed in fixed sequence with well-defined interfaces and shared tool access (RAG, HITL), mirroring the harness pattern of orchestrating heterogeneous agents through typed phases. The Hypothesis-Critic pairing at both Divide and Combine stages is a reusable harness primitive—an adversarial self-correction loop—that could be extracted and reused in other agentic pipelines. The framework also demonstrates how HITL can be integrated into a harness as a first-class tool call rather than an out-of-band interrupt, informing harness designers who want to make human feedback composable with automated agent steps. The theoretical SHD decomposition (Theorem 2) is a rare formal analysis of how error propagates across harness stages, useful for reasoning about correctness guarantees in multi-agent pipelines generally.