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Stochastic Linear Optimization with Adversarial Corruption

arXiv 1909.02109 ↗First posted 4 Sep 2019cs.LG stat.MLcited by 24

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Abstract (arXiv)

We extend the model of stochastic bandits with adversarial corruption (Lykouriset al., 2018) to the stochastic linear optimization problem (Dani et al., 2008). Our algorithm is agnostic to the amount of corruption chosen by the adaptive adversary. The regret of the algorithm only increases linearly in the amount of corruption. Our algorithm involves using L"owner-John's ellipsoid for exploration and dividing time horizon into epochs with exponentially increasing size to limit the influence of corruption.

Key facts. Cited by 24 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Sep 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 8; 2022: 5; 2023: 6; 2024: 3; 2025: 0; 2026: 2.

24 papers.

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  1. 2022Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptionscited by 51
  2. 2021Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneouslycited by 48
  3. 2021A Model Selection Approach for Corruption Robust Reinforcement Learningcited by 45
  4. 2021Robust Stochastic Linear Contextual Bandits Under Adversarial Attackscited by 33
  5. 2022Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processescited by 33
  6. 2021On Optimal Robustness to Adversarial Corruption in Online Decision Problemscited by 21
  7. 2021Linear Contextual Bandits with Adversarial Corruptionscited by 21
  8. 2021Improved Corruption Robust Algorithms for Episodic Reinforcement Learningcited by 20
  9. 2022Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithmscited by 19
  10. 2023Robust Lipschitz Bandits to Adversarial Corruptionscited by 15
  11. 2023Best-of-Three-Worlds Linear Bandit Algorithm with Variance-Adaptive Regret Boundscited by 14
  12. 2023Best-of-three-worlds Analysis for Linear Bandits with Follow-the-regularized-leader Algorithmcited by 12
12 more
  1. 2021Bias-Robust Bayesian Optimization via Dueling Banditscited by 11
  2. 2022A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Banditscited by 11
  3. 2024Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedbackcited by 9
  4. 2024Corruption-Robust Linear Bandits: Minimax Optimality and Gap-Dependent Misspecificationcited by 7
  5. 2021Cooperative Stochastic Multi-agent Multi-armed Bandits Robust to Adversarial Corruptionscited by 5
  6. 2022Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimizationcited by 4
  7. 2023Robust Causal Bandits for Linear Modelscited by 4
  8. 2023Online Corrupted User Detection and Regret Minimizationcited by 3
  9. 2024Improved Bound for Robust Causal Bandits with Linear Modelscited by 2
  10. 2023Robust and differentially private stochastic linear banditscited by 0
  11. 2026Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noisecited by 0
  12. 2026Corruption-Robust Sparse Linear Contextual Bandits with Knapsack Constraintscited by 0