Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise

• URL: http://arxiv.org/abs/2603.15596v1
• Date: Mon, 16 Mar 2026 17:53:06 GMT
• Title: Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise
• Abstract summary: We study linear contextual bandits under adversarial corruption and heavy-tailed noise.<n>Our algorithm achieves robustness to both adversarial corruption and heavy-tailed noise.
• Score: 5.296855056439798
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+ε)$-th moments for some $ε\in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise relies on a finite variance (i.e., finite second-moment) assumption and suffers from computational inefficiency. We propose a computationally efficient algorithm based on online mirror descent that achieves robustness to both adversarial corruption and heavy-tailed noise. While the existing algorithm incurs $\mathcal{O}(t\log T)$ computational cost, our algorithm reduces this to $\mathcal{O}(1)$ per round. We establish an additive regret bound consisting of a term depending on the $(1+ε)$-moment bound of the noise and a term depending on the total amount of corruption. In particular, when $ε= 1$, our result recovers existing guarantees under finite-variance assumptions. When no corruption is present, it matches the best-known rates for linear contextual bandits with heavy-tailed noise. Moreover, the algorithm requires no prior knowledge of the noise moment bound or the total amount of corruption and still guarantees sublinear regret.

Related papers

• Corruption-Robust Offline Reinforcement Learning with General Function Approximation [60.91257031278004]
  We investigate the problem of corruption in offline reinforcement learning (RL) with general function approximation. Our goal is to find a policy that is robust to such corruption and minimizes the suboptimality gap with respect to the optimal policy for the uncorrupted Markov decision processes (MDPs)
  arXiv  Detail & Related papers  (2023-10-23T04:07:26Z)
• Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes [59.61248760134937]
  We propose an efficient algorithm to achieve a regret of $tildeO(sqrtT+zeta)$. The proposed algorithm relies on the recently developed uncertainty-weighted least-squares regression from linear contextual bandit. We generalize our algorithm to the episodic MDP setting and first achieve an additive dependence on the corruption level $zeta$.
  arXiv  Detail & Related papers  (2022-12-12T15:04:56Z)
• Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions [98.75618795470524]
  We study the linear contextual bandit problem in the presence of adversarial corruption. We propose a new algorithm based on the principle of optimism in the face of uncertainty.
  arXiv  Detail & Related papers  (2022-05-13T17:58:58Z)
• A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits [118.22458816174144]
  We propose a novel robust elimination-type algorithm that runs in epochs, combines exploration with infrequent switching to select a small subset of actions, and plays each action for multiple time instants. Our algorithm, GP Robust Phased Elimination (RGP-PE), successfully balances robustness to corruptions with exploration and exploitation. We perform the first empirical study of robustness in the corrupted GP bandit setting, and show that our algorithm is robust against a variety of adversarial attacks.
  arXiv  Detail & Related papers  (2022-02-03T21:19:36Z)
• On the power of adaptivity in statistical adversaries [18.973408992715203]
  We study a fundamental question concerning adversarial noise models in statistical problems. Can the behavior of an algorithm $mathcalA'$ in the presence of oblivious adversaries always be well-approximated by that of an algorithm $mathcalA'$ in the presence of adaptive adversaries?
  arXiv  Detail & Related papers  (2021-11-19T18:26:25Z)
• Breaking the Moments Condition Barrier: No-Regret Algorithm for Bandits with Super Heavy-Tailed Payoffs [27.636407641546914]
  We propose a novel robust statistical estimator, mean of medians, which estimates a random variable by computing the empirical mean of a sequence of empirical medians. We show that the regret bound is near-optimal even with very heavy-tailed noise.
  arXiv  Detail & Related papers  (2021-10-26T17:30:44Z)
• Linear Contextual Bandits with Adversarial Corruptions [91.38793800392108]
  We study the linear contextual bandit problem in the presence of adversarial corruption. We present a variance-aware algorithm that is adaptive to the level of adversarial contamination $C$.
  arXiv  Detail & Related papers  (2021-10-25T02:53:24Z)
• Stochastic Linear Bandits Robust to Adversarial Attacks [117.665995707568]
  We provide two variants of a Robust Phased Elimination algorithm, one that knows $C$ and one that does not. We show that both variants attain near-optimal regret in the non-corrupted case $C = 0$, while incurring additional additive terms respectively. In a contextual setting, we show that a simple greedy algorithm is provably robust with a near-optimal additive regret term, despite performing no explicit exploration and not knowing $C$.
  arXiv  Detail & Related papers  (2020-07-07T09:00:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.