# Regret Bounds for Batched Bandits

arXiv: https://arxiv.org/abs/1910.04959 · HTML: https://mlsanity.com/paper/1910.04959/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2019.

## Built on by (most cited first, 30 of 49)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints](https://mlsanity.com/paper/2101.02195/) (2021)
- [Gaussian Process Bandit Optimization with Few Batches](https://mlsanity.com/paper/2110.07788/) (2021)
- [Sample-Efficient Reinforcement Learning with loglog(T) Switching Cost](https://mlsanity.com/paper/2202.06385/) (2022)
- [Differentially Private Multi-Armed Bandits in the Shuffle Model](https://mlsanity.com/paper/2106.02900/) (2021)
- [Towards Deployment-Efficient Reinforcement Learning: Lower Bound and Optimality](https://mlsanity.com/paper/2202.06450/) (2022)
- [Replicable Bandits](https://mlsanity.com/paper/2210.01898/) (2022)
- [Lipschitz Bandits with Batched Feedback](https://mlsanity.com/paper/2110.09722/) (2021)
- [Parallelizing Thompson Sampling](https://mlsanity.com/paper/2106.01420/) (2021)
- [An Algorithm for Stochastic and Adversarial Bandits with Switching Costs](https://mlsanity.com/paper/2102.09864/) (2021)
- [Batched Thompson Sampling](https://mlsanity.com/paper/2110.00202/) (2021)
- [Differentially Private Stochastic Linear Bandits: (Almost) for Free](https://mlsanity.com/paper/2207.03445/) (2022)
- [Design of Experiments for Stochastic Contextual Linear Bandits](https://mlsanity.com/paper/2107.09912/) (2021)
- [Solving Multi-Arm Bandit Using a Few Bits of Communication](https://mlsanity.com/paper/2111.06067/) (2021)
- [Better Best of Both Worlds Bounds for Bandits with Switching Costs](https://mlsanity.com/paper/2206.03098/) (2022)
- [Near-Optimal Deployment Efficiency in Reward-Free Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2210.00701/) (2022)
- [Batched Dueling Bandits](https://mlsanity.com/paper/2202.10660/) (2022)
- [Almost Optimal Batch-Regret Tradeoff for Batch Linear Contextual Bandits](https://mlsanity.com/paper/2110.08057/) (2021)
- [A Lipschitz Bandits Approach for Continuous Hyperparameter Optimization](https://mlsanity.com/paper/2302.01539/) (2023)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Optimal Batched Linear Bandits](https://mlsanity.com/paper/2406.04137/) (2024)
- [Falcon: Fair Active Learning using Multi-armed Bandits](https://mlsanity.com/paper/2401.12722/) (2024)
- [Reward Imputation with Sketching for Contextual Batched Bandits](https://mlsanity.com/paper/2210.06719/) (2022)
- [Experiment Planning with Function Approximation](https://mlsanity.com/paper/2401.05193/) (2024)
- [Multi-Drafter Speculative Decoding with Alignment Feedback](https://mlsanity.com/paper/2604.05417/) (2026)
- [The Impact of Batch Learning in Stochastic Linear Bandits](https://mlsanity.com/paper/2202.06657/) (2022)
- [Cooperative Multi-agent Bandits: Distributed Algorithms with Optimal Individual Regret and Constant Communication Costs](https://mlsanity.com/paper/2308.04314/) (2023)
- [Adversarial Online Learning with Temporal Feedback Graphs](https://mlsanity.com/paper/2407.00571/) (2024)
- [Batched Kernelized Bandits: Refinements and Extensions](https://mlsanity.com/paper/2603.12627/) (2026)
- [An Asymptotically Optimal Batched Algorithm for the Dueling Bandit Problem](https://mlsanity.com/paper/2209.12108/) (2022)
- [Adaptive Experimentation at Scale: A Computational Framework for Flexible Batches](https://mlsanity.com/paper/2303.11582/) (2023)

## Abstract (arXiv)

We present simple and efficient algorithms for the batched stochastic multi-armed bandit and batched stochastic linear bandit problems. We prove bounds for their expected regrets that improve over the best-known regret bounds for any number of batches. In particular, our algorithms in both settings achieve the optimal expected regrets by using only a logarithmic number of batches. We also study the batched adversarial multi-armed bandit problem for the first time and find the optimal regret, up to logarithmic factors, of any algorithm with predetermined batch sizes.