# Stochastic Linear Bandits Robust to Adversarial Attacks

arXiv: https://arxiv.org/abs/2007.03285 · HTML: https://mlsanity.com/paper/2007.03285/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 30 of 65)

- [Federated Linear Contextual Bandits](https://mlsanity.com/paper/2110.14177/) (2021)
- [Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2205.06811/) (2022)
- [Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneously](https://mlsanity.com/paper/2102.05858/) (2021)
- [A Model Selection Approach for Corruption Robust Reinforcement Learning](https://mlsanity.com/paper/2110.03580/) (2021)
- [Robust Stochastic Linear Contextual Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2106.02978/) (2021)
- [Corruption-Robust Algorithms with Uncertainty Weighting for Nonlinear Contextual Bandits and Markov Decision Processes](https://mlsanity.com/paper/2212.05949/) (2022)
- [Corruption-Robust Offline Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2310.14550/) (2023)
- [Defense Against Reward Poisoning Attacks in Reinforcement Learning](https://mlsanity.com/paper/2102.05776/) (2021)
- [On Optimal Robustness to Adversarial Corruption in Online Decision Problems](https://mlsanity.com/paper/2109.10963/) (2021)
- [Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2110.12615/) (2021)
- [Understanding the Limits of Poisoning Attacks in Episodic Reinforcement Learning](https://mlsanity.com/paper/2208.13663/) (2022)
- [Improved Corruption Robust Algorithms for Episodic Reinforcement Learning](https://mlsanity.com/paper/2102.06875/) (2021)
- [Exploiting Heterogeneity in Robust Federated Best-Arm Identification](https://mlsanity.com/paper/2109.05700/) (2021)
- [Reward Poisoning Attacks on Offline Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2206.01888/) (2022)
- [Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithms](https://mlsanity.com/paper/2211.05632/) (2022)
- [Robust Lipschitz Bandits to Adversarial Corruptions](https://mlsanity.com/paper/2305.18543/) (2023)
- [Best-of-Three-Worlds Linear Bandit Algorithm with Variance-Adaptive Regret Bounds](https://mlsanity.com/paper/2302.12370/) (2023)
- [Best-of-three-worlds Analysis for Linear Bandits with Follow-the-regularized-leader Algorithm](https://mlsanity.com/paper/2303.06825/) (2023)
- [Towards Robust Model-Based Reinforcement Learning Against Adversarial Corruption](https://mlsanity.com/paper/2402.08991/) (2024)
- [Bias-Robust Bayesian Optimization via Dueling Bandits](https://mlsanity.com/paper/2105.11802/) (2021)
- [A Robust Phased Elimination Algorithm for Corruption-Tolerant Gaussian Process Bandits](https://mlsanity.com/paper/2202.01850/) (2022)
- [Best-of-Both-Worlds Algorithms for Linear Contextual Bandits](https://mlsanity.com/paper/2312.15433/) (2023)
- [Syndicated Bandits: A Framework for Auto Tuning Hyper-parameters in Contextual Bandit Algorithms](https://mlsanity.com/paper/2106.02979/) (2021)
- [When Are Linear Stochastic Bandits Attackable?](https://mlsanity.com/paper/2110.09008/) (2021)
- [Saving Stochastic Bandits from Poisoning Attacks via Limited Data Verification](https://mlsanity.com/paper/2102.07711/) (2021)
- [Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback](https://mlsanity.com/paper/2404.10776/) (2024)
- [Game Redesign in No-regret Game Playing](https://mlsanity.com/paper/2110.11763/) (2021)
- [Corruption-Robust Linear Bandits: Minimax Optimality and Gap-Dependent Misspecification](https://mlsanity.com/paper/2410.07533/) (2024)
- [Combinatorial Bandits under Strategic Manipulations](https://mlsanity.com/paper/2102.12722/) (2021)
- [Federated Multi-Armed Bandits Under Byzantine Attacks](https://mlsanity.com/paper/2205.04134/) (2022)

## Abstract (arXiv)

We consider a stochastic linear bandit problem in which the rewards are not only subject to random noise, but also adversarial attacks subject to a suitable budget C (i.e., an upper bound on the sum of corruption magnitudes across the time horizon). We provide two variants of a Robust Phased Elimination algorithm, one that knows C and one that does not. Both variants are shown to attain near-optimal regret in the non-corrupted case C = 0, while incurring additional additive terms respectively having a linear and quadratic dependency on C in general. We present algorithm independent lower bounds showing that these additive terms are near-optimal. In addition, in a contextual setting, we revisit a setup of diverse contexts, and 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.