# Delayed Feedback in Generalised Linear Bandits Revisited

arXiv: https://arxiv.org/abs/2207.10786 · HTML: https://mlsanity.com/paper/2207.10786/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 29 references that are in the map.
- First posted on arXiv 21 Jul 2022.

## Builds on (most cited first, 8 of 8)

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Linear Bandits with Stochastic Delayed Feedback](https://mlsanity.com/paper/1807.02089/) (2018)
- [Stochastic Bandit Models for Delayed Conversions](https://mlsanity.com/paper/1706.09186/) (2017)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [Delay-Adaptive Learning in Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2003.05174/) (2020)

## Built on by (most cited first, 23 of 23)

- [SpecDec++: Boosting Speculative Decoding via Adaptive Candidate Lengths](https://mlsanity.com/paper/2405.19715/) (2024)
- [A Unified Analysis of Nonstochastic Delayed Feedback for Combinatorial Semi-Bandits, Linear Bandits, and MDPs](https://mlsanity.com/paper/2305.08629/) (2023)
- [Delayed Feedback in Kernel Bandits](https://mlsanity.com/paper/2302.00392/) (2023)
- [A Reduction-based Framework for Sequential Decision Making with Delayed Feedback](https://mlsanity.com/paper/2302.01477/) (2023)
- [Delay-Adapted Policy Optimization and Improved Regret for Adversarial MDP with Delayed Bandit Feedback](https://mlsanity.com/paper/2305.07911/) (2023)
- [Delay as Payoff in MAB](https://mlsanity.com/paper/2408.15158/) (2024)
- [Regret Bounds for Adversarial Contextual Bandits with General Function Approximation and Delayed Feedback](https://mlsanity.com/paper/2510.09127/) (2025)
- [Efficient Reinforcement Learning with Impaired Observability: Learning to Act with Delayed and Missing State Observations](https://mlsanity.com/paper/2306.01243/) (2023)
- [Posterior Sampling with Delayed Feedback for Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2310.18919/) (2023)
- [Biased Dueling Bandits with Stochastic Delayed Feedback](https://mlsanity.com/paper/2408.14603/) (2024)
- [Improved Best-of-Both-Worlds Regret for Bandits with Delayed Feedback](https://mlsanity.com/paper/2505.24193/) (2025)
- [Stochastic Contextual Bandits with Long Horizon Rewards](https://mlsanity.com/paper/2302.00814/) (2023)
- [Comparative Performance of Collaborative Bandit Algorithms: Effect of Sparsity and Exploration Intensity](https://mlsanity.com/paper/2410.12086/) (2024)
- [Lipschitz Bandits with Stochastic Delayed Feedback](https://mlsanity.com/paper/2510.00309/) (2025)
- [Batched Stochastic Linear Bandits with 1-Bit Communication Constraints](https://mlsanity.com/paper/2605.30976/) (2026)
- [Risk-averse learning with delayed feedback](https://mlsanity.com/paper/2409.16866/) (2024)
- [Neural Contextual Bandits Under Delayed Feedback Constraints](https://mlsanity.com/paper/2504.12086/) (2025)
- [Linear Bandits with Non-i.i.d. Noise](https://mlsanity.com/paper/2505.20017/) (2025)
- [Robust Remote Reinforcement Learning over Unreliable Communication Channels using Homomorphic State Encoding](https://mlsanity.com/paper/2508.07722/) (2025)
- [Minimax Optimal Strategy for Delayed Observations in Online Reinforcement Learning](https://mlsanity.com/paper/2603.03480/) (2026)
- [Robust Linear Dueling Bandits with Post-serving Context under Unknown Delays and Adversarial Corruptions](https://mlsanity.com/paper/2605.01752/) (2026)
- [Near-Optimal Stochastic Linear Bandits with Delay](https://mlsanity.com/paper/2606.16656/) (2026)
- [Provably Efficient Reinforcement Learning in Continuous-Time Episodic MDPs with Poisson Decision Epochs](https://mlsanity.com/paper/2609.23127/) (2026)

## Abstract (arXiv)

The stochastic generalised linear bandit is a well-understood model for sequential decision-making problems, with many algorithms achieving near-optimal regret guarantees under immediate feedback. However, the stringent requirement for immediate rewards is unmet in many real-world applications where the reward is almost always delayed. We study the phenomenon of delayed rewards in generalised linear bandits in a theoretical manner. We show that a natural adaptation of an optimistic algorithm to the delayed feedback achieves a regret bound where the penalty for the delays is independent of the horizon. This result significantly improves upon existing work, where the best known regret bound has the delay penalty increasing with the horizon. We verify our theoretical results through experiments on simulated data.