mlsanityData to 7 Oct 2026

Robust Causal Bandits for Linear Models

arXiv 2310.19794 ↗First posted 30 Oct 2023stat.ML cs.LGcited by 4

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Abstract (arXiv)

Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is that the causal models remain constant over time. However, this assumption does not necessarily hold in complex systems, which constantly undergo temporal model fluctuations. This paper addresses the robustness of CBs to such model fluctuations. The focus is on causal systems with linear structural equation models (SEMs). The SEMs and the time-varying pre- and post-interventional statistical models are all unknown. Cumulative regret is adopted as the design criteria, based on which the objective is to design a sequence of interventions that incur the smallest cumulative regret with respect to an oracle aware of the entire causal model and its fluctuations. First, it is established that the existing approaches fail to maintain regret sub-linearity with even a few instances of model deviation. Specifically, when the number of instances with model deviation is as few as T^frac12L, where T is the time horizon and L is the longest causal path in the graph, the existing algorithms will have linear regret in T. Next, a robust CB algorithm is designed, and its regret is analyzed, where upper and information-theoretic lower bounds on the regret are established. Specifically, in a graph with N nodes and maximum degree d, under a general measure of model deviation C, the cumulative regret is upper bounded by tildeO(d^L-frac12(√NT + NC)) and lower bounded by Omega(d^fracL2-2max√T,d2C). Comparing these bounds establishes that the proposed algorithm achieves nearly optimal tildeO(√T) regret when C is o(√T) and maintains sub-linear regret for a broader range of C.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 28 of its 39 references that are in the map. First posted on arXiv 30 Oct 2023.

Builds on

28 of 39 references.

References · 28

  1. 2019Learning with Good Feature Representations in Bandits and in RL with a Generative Modelcited by 124
  2. 2020CausalWorld: A Robotic Manipulation Benchmark for Causal Structure and Transfer Learningcited by 109
  3. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 100
  4. 2019Weighted Linear Bandits for Non-Stationary Environmentscited by 84
  5. 2021Adapting to Misspecification in Contextual Banditscited by 81
  6. 2020Stochastic Linear Bandits Robust to Adversarial Attackscited by 65
  7. 2022Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptionscited by 51
  8. 2021Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneouslycited by 48
  9. 2018Causal Discovery in the Presence of Missing Datacited by 46
  10. 2021A Model Selection Approach for Corruption Robust Reinforcement Learningcited by 45
  11. 2017Learning Graph-Level Representation for Drug Discoverycited by 43
  12. 2017Misspecified Linear Banditscited by 41
16 more
  1. 2020Budgeted and Non-budgeted Causal Banditscited by 38
  2. 2021Causal Bandits with Unknown Graph Structurecited by 37
  3. 2021Robust Stochastic Linear Contextual Bandits Under Adversarial Attackscited by 33
  4. 2022Model-based Causal Bayesian Optimizationcited by 26
  5. 2019Stochastic Linear Optimization with Adversarial Corruptioncited by 23
  6. 2021Adapting to Misspecification in Contextual Bandits with Offline Regression Oraclescited by 21
  7. 2021Linear Contextual Bandits with Adversarial Corruptionscited by 21
  8. 2022Causal Bandits for Linear Structural Equation Modelscited by 19
  9. 2022Adaptively Exploiting d-Separators with Causal Banditscited by 18
  10. 2020Causal Bandits without prior knowledge using separating setscited by 17
  11. 2021Matching a Desired Causal State via Shift Interventionscited by 16
  12. 2022Combinatorial Causal Banditscited by 16
  13. 2021A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounderscited by 15
  14. 2023Causal Bandits without Graph Learningcited by 10
  15. 2017Causal Discovery in the Presence of Measurement Error: Identifiability Conditionscited by 9
  16. 2023Combinatorial Causal Bandits without Graph Skeletoncited by 7

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Cited by year

Citing papers per year: 2024: 3; 2025: 1.

4 papers.

  1. 2024Linear Causal Bandits: Unknown Graph and Soft Interventionscited by 5
  2. 2024Improved Bound for Robust Causal Bandits with Linear Modelscited by 2
  3. 2024Asymmetric Graph Error Control with Low Complexity in Causal Banditscited by 2
  4. 2025Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanismscited by 0