mlsanityData to 14 Oct 2026

FOCUS: Fixed-Confidence Online Causal Learning Using Sequential Adaptive Interventions

arXiv 2609.32165 ↗First posted 26 Sep 2026stat.ML cs.LGcited by 0

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Abstract (arXiv)

We study fully online fixed-confidence causal discovery without any historical observational data. Starting from zero samples, the learner sequentially selects interventions to recover both the causal DAG and its edge weights under a linear-Gaussian structural equation model. We establish an instance-dependent lower bound for any (ε,δ)-correct algorithm and propose textscFOCUS, which adaptively allocates interventions through an online max--min game. A key contribution is a computable concentration inequality for the accumulated KL divergence involving causal parameters shared across interventions. We prove that textscFOCUS is (ε,δ)-correct and that its expected stopping time matches the lower bound in its Theta(log(1/δ)) dependence up to an instance-dependent constant. Experiments demonstrate improved structure and edge-weight recovery and confirm the predicted stopping-time trend. Our codes are available on https://anonymous.4open.science/r/FOCUScode-76E5

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References · 20

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2014On the Complexity of Best Arm Identification in Multi-Armed Bandit Modelscited by 286
  3. 2016Optimal Best Arm Identification with Fixed Confidencecited by 239
  4. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  5. 2013Follow the Leader If You Can, Hedge If You Mustcited by 70
  6. 2015Learning Causal Graphs with Small Interventionscited by 63
  7. 2019Non-Asymptotic Pure Exploration by Solving Gamescited by 63
  8. 2019ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discoverycited by 52
  9. 2022Interventions, Where and How? Experimental Design for Causal Models at Scalecited by 49
  10. 2017Cost-Optimal Learning of Causal Graphscited by 44
  11. 2021Learning Neural Causal Models with Active Interventionscited by 40
  12. 2017Budgeted Experiment Design for Causal Structure Learningcited by 38
8 more
  1. 2020Active Structure Learning of Causal DAGs via Directed Clique Treecited by 38
  2. 2022Active Bayesian Causal Inferencecited by 35
  3. 2018Experimental Design for Cost-Aware Learning of Causal Graphscited by 25
  4. 2022Verification and search algorithms for causal DAGscited by 18
  5. 2021Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learningcited by 17
  6. 2023Adaptivity Complexity for Causal Graph Discoverycited by 7
  7. 2022Trust Your nabla: Gradient-based Intervention Targeting for Causal Discoverycited by 5
  8. 2024Adaptive Online Experimental Design for Causal Discoverycited by 5

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