Lipschitz Bandits with Stochastic Delayed Feedback
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911439001747456 |
|---|---|
| author | Liu, Zhongxuan Kang, Yue Lee, Thomas C. M. |
| author_facet | Liu, Zhongxuan Kang, Yue Lee, Thomas C. M. |
| contents | The Lipschitz bandit problem extends stochastic bandits to a continuous action set defined over a metric space, where the expected reward function satisfies a Lipschitz condition. In this work, we introduce a new problem of Lipschitz bandit in the presence of stochastic delayed feedback, where the rewards are not observed immediately but after a random delay. We consider both bounded and unbounded stochastic delays, and design algorithms that attain sublinear regret guarantees in each setting. For bounded delays, we propose a delay-aware zooming algorithm that retains the optimal performance of the delay-free setting up to an additional term that scales with the maximal delay $τ_{\max}$. For unbounded delays, we propose a novel phased learning strategy that accumulates reliable feedback over carefully scheduled intervals, and establish a regret lower bound showing that our method is nearly optimal up to logarithmic factors. Finally, we present experimental results to demonstrate the efficiency of our algorithms under various delay scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz Bandits with Stochastic Delayed Feedback Liu, Zhongxuan Kang, Yue Lee, Thomas C. M. Machine Learning The Lipschitz bandit problem extends stochastic bandits to a continuous action set defined over a metric space, where the expected reward function satisfies a Lipschitz condition. In this work, we introduce a new problem of Lipschitz bandit in the presence of stochastic delayed feedback, where the rewards are not observed immediately but after a random delay. We consider both bounded and unbounded stochastic delays, and design algorithms that attain sublinear regret guarantees in each setting. For bounded delays, we propose a delay-aware zooming algorithm that retains the optimal performance of the delay-free setting up to an additional term that scales with the maximal delay $τ_{\max}$. For unbounded delays, we propose a novel phased learning strategy that accumulates reliable feedback over carefully scheduled intervals, and establish a regret lower bound showing that our method is nearly optimal up to logarithmic factors. Finally, we present experimental results to demonstrate the efficiency of our algorithms under various delay scenarios. |
| title | Lipschitz Bandits with Stochastic Delayed Feedback |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.00309 |