Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Tani, Naoto Futami, Futoshi |
| author_facet | Tani, Naoto Futami, Futoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise Tani, Naoto Futami, Futoshi Machine Learning 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. |
| title | Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.15596 |