mlsanityData to 14 Oct 2026

Additive Causal Bandits with Unknown Graph

arXiv 2306.07858 ↗First posted 13 Jun 2023cs.LG stat.MLcited by 10

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Abstract (arXiv)

We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 14 of its 27 references that are in the map. First posted on arXiv 13 Jun 2023.

Builds on

14 of 27 references.

References · 14

  1. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  2. 2019Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?cited by 140
  3. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 101
  4. 2014Best-Arm Identification in Linear Banditscited by 100
  5. 2019Sequential Experimental Design for Transductive Linear Banditscited by 91
  6. 2017Fully adaptive algorithm for pure exploration in linear banditscited by 43
  7. 2020Budgeted and Non-budgeted Causal Banditscited by 38
  8. 2021Causal Bandits with Unknown Graph Structurecited by 37
  9. 2017Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approachcited by 19
  10. 2022Adaptively Exploiting d-Separators with Causal Banditscited by 18
  11. 2020Causal Bandits without prior knowledge using separating setscited by 17
  12. 2021A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounderscited by 15
2 more
  1. 2022Combinatorial Pure Exploration of Causal Banditscited by 9
  2. 2015Extended Conditional Independence and Applications in Causal Inferencecited by 7

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Cited by year

Citing papers per year: 2024: 8; 2025: 2.

10 papers.

  1. 2024Causal Bandits with General Causal Models and Interventionscited by 7
  2. 2024Linear Causal Bandits: Unknown Graph and Soft Interventionscited by 5
  3. 2024Partial Structure Discovery is Sufficient for No-regret Learning in Causal Banditscited by 5
  4. 2024Improved Bound for Robust Causal Bandits with Linear Modelscited by 2
  5. 2024Causal Bandits: The Pareto Optimal Frontier of Adaptivity, a Reduction to Linear Bandits, and Limitations around Unknown Marginalscited by 2
  6. 2024Asymmetric Graph Error Control with Low Complexity in Causal Banditscited by 2
  7. 2025Graph Learning Is Suboptimal in Causal Banditscited by 2
  8. 2024Causal Contextual Bandits with Adaptive Contextcited by 1
  9. 2024Graph Agnostic Causal Bayesian Optimisationcited by 1
  10. 2025Causal Bayesian Optimization with Unknown Graphscited by 0