# Stochastic bandits robust to adversarial corruptions

arXiv: https://arxiv.org/abs/1803.09353 · HTML: https://mlsanity.com/paper/1803.09353/

## Key facts

- Cited by 119 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2018.

## Built on by (most cited first, 30 of 119)

- [Adapting to Misspecification in Contextual Bandits](https://mlsanity.com/paper/2107.05745/) (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)
- [Bayesian decision-making under misspecified priors with applications to meta-learning](https://mlsanity.com/paper/2107.01509/) (2021)
- [The best of both worlds: stochastic and adversarial episodic MDPs with unknown transition](https://mlsanity.com/paper/2106.04117/) (2021)
- [Robust Stochastic Linear Contextual Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2106.02978/) (2021)
- [On the Complexity of Adversarial Decision Making](https://mlsanity.com/paper/2206.13063/) (2022)
- [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)
- [Robust Policy Gradient against Strong Data Corruption](https://mlsanity.com/paper/2102.05800/) (2021)
- [A Blackbox Approach to Best of Both Worlds in Bandits and Beyond](https://mlsanity.com/paper/2302.09739/) (2023)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Nearly Optimal Best-of-Both-Worlds Algorithms for Online Learning with Feedback Graphs](https://mlsanity.com/paper/2206.00873/) (2022)
- [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)
- [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)
- [Best-of-Both-Worlds Algorithms for Partial Monitoring](https://mlsanity.com/paper/2207.14550/) (2022)
- [Adaptively Exploiting d-Separators with Causal Bandits](https://mlsanity.com/paper/2202.05100/) (2022)
- [Improved Analysis of the Tsallis-INF Algorithm in Stochastically Constrained Adversarial Bandits and Stochastic Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2103.12487/) (2021)
- [One More Step Towards Reality: Cooperative Bandits with Imperfect Communication](https://mlsanity.com/paper/2111.12482/) (2021)
- [Stability-penalty-adaptive follow-the-regularized-leader: Sparsity, game-dependency, and best-of-both-worlds](https://mlsanity.com/paper/2305.17301/) (2023)
- [Robust Lipschitz Bandits to Adversarial Corruptions](https://mlsanity.com/paper/2305.18543/) (2023)
- [Multi-channel Autobidding with Budget and ROI Constraints](https://mlsanity.com/paper/2302.01523/) (2023)
- [Best-of-Three-Worlds Linear Bandit Algorithm with Variance-Adaptive Regret Bounds](https://mlsanity.com/paper/2302.12370/) (2023)
- [Can Q-Learning be Improved with Advice?](https://mlsanity.com/paper/2110.13052/) (2021)
- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [Bandit Algorithms for Precision Medicine](https://mlsanity.com/paper/2108.04782/) (2021)

## Abstract (arXiv)

We introduce a new model of stochastic bandits with adversarial corruptions which aims to capture settings where most of the input follows a stochastic pattern but some fraction of it can be adversarially changed to trick the algorithm, e.g., click fraud, fake reviews and email spam. The goal of this model is to encourage the design of bandit algorithms that (i) work well in mixed adversarial and stochastic models, and (ii) whose performance deteriorates gracefully as we move from fully stochastic to fully adversarial models. In our model, the rewards for all arms are initially drawn from a distribution and are then altered by an adaptive adversary. We provide a simple algorithm whose performance gracefully degrades with the total corruption the adversary injected in the data, measured by the sum across rounds of the biggest alteration the adversary made in the data in that round; this total corruption is denoted by C. Our algorithm provides a guarantee that retains the optimal guarantee (up to a logarithmic term) if the input is stochastic and whose performance degrades linearly to the amount of corruption C, while crucially being agnostic to it. We also provide a lower bound showing that this linear degradation is necessary if the algorithm achieves optimal performance in the stochastic setting (the lower bound works even for a known amount of corruption, a special case in which our algorithm achieves optimal performance without the extra logarithm).