# An algorithm with nearly optimal pseudo-regret for both stochastic and adversarial bandits

arXiv: https://arxiv.org/abs/1605.08722 · HTML: https://mlsanity.com/paper/1605.08722/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2016.

## Built on by (most cited first, 30 of 47)

- [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)
- [The best of both worlds: stochastic and adversarial episodic MDPs with unknown transition](https://mlsanity.com/paper/2106.04117/) (2021)
- [A Blackbox Approach to Best of Both Worlds in Bandits and Beyond](https://mlsanity.com/paper/2302.09739/) (2023)
- [Tracking Most Significant Arm Switches in Bandits](https://mlsanity.com/paper/2112.13838/) (2021)
- [A Best-of-Both-Worlds Algorithm for Bandits with Delayed Feedback](https://mlsanity.com/paper/2206.14906/) (2022)
- [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)
- [An Algorithm for Stochastic and Adversarial Bandits with Switching Costs](https://mlsanity.com/paper/2102.09864/) (2021)
- [Adaptive Best-of-Both-Worlds Algorithm for Heavy-Tailed Multi-Armed Bandits](https://mlsanity.com/paper/2201.11921/) (2022)
- [A Near-Optimal Best-of-Both-Worlds Algorithm for Online Learning with Feedback Graphs](https://mlsanity.com/paper/2206.00557/) (2022)
- [Best of Both Worlds Policy Optimization](https://mlsanity.com/paper/2302.09408/) (2023)
- [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)
- [Better Best of Both Worlds Bounds for Bandits with Switching Costs](https://mlsanity.com/paper/2206.03098/) (2022)
- [Pareto Regret Analyses in Multi-objective Multi-armed Bandit](https://mlsanity.com/paper/2212.00884/) (2022)
- [Adversarially Robust Multi-Armed Bandit Algorithm with Variance-Dependent Regret Bounds](https://mlsanity.com/paper/2206.06810/) (2022)
- [Best-of-three-worlds Analysis for Linear Bandits with Follow-the-regularized-leader Algorithm](https://mlsanity.com/paper/2303.06825/) (2023)
- [Best of Both Worlds Model Selection](https://mlsanity.com/paper/2206.14912/) (2022)
- [Beyond Primal-Dual Methods in Bandits with Stochastic and Adversarial Constraints](https://mlsanity.com/paper/2405.16118/) (2024)
- [Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback](https://mlsanity.com/paper/2404.10776/) (2024)
- [Robust Bandit Learning with Imperfect Context](https://mlsanity.com/paper/2102.05018/) (2021)
- [Corruption-Robust Linear Bandits: Minimax Optimality and Gap-Dependent Misspecification](https://mlsanity.com/paper/2410.07533/) (2024)
- [Simultaneously Learning Stochastic and Adversarial Bandits with General Graph Feedback](https://mlsanity.com/paper/2206.07908/) (2022)
- [Cooperative Stochastic Multi-agent Multi-armed Bandits Robust to Adversarial Corruptions](https://mlsanity.com/paper/2106.04207/) (2021)
- [Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences](https://mlsanity.com/paper/2202.06694/) (2022)
- [Simple Combinatorial Algorithms for Combinatorial Bandits: Corruptions and Approximations](https://mlsanity.com/paper/2106.06712/) (2021)
- [Best-of-All-Worlds Bounds for Online Learning with Feedback Graphs](https://mlsanity.com/paper/2107.09572/) (2021)
- [Best of Many Worlds Guarantees for Online Learning with Knapsacks](https://mlsanity.com/paper/2202.13710/) (2022)
- [LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits](https://mlsanity.com/paper/2403.03219/) (2024)

## Abstract (arXiv)

We present an algorithm that achieves almost optimal pseudo-regret bounds against adversarial and stochastic bandits. Against adversarial bandits the pseudo-regret is O(K√n log n) and against stochastic bandits the pseudo-regret is O(sumi (log n)/Deltai). We also show that no algorithm with O(log n) pseudo-regret against stochastic bandits can achieve tildeO(√n) expected regret against adaptive adversarial bandits. This complements previous results of Bubeck and Slivkins (2012) that show tildeO(√n) expected adversarial regret with O((log n)2) stochastic pseudo-regret.