Lipschitz Bandits with Stochastic Delayed Feedback

Fuente: arXiv
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Main Authors: Liu, Zhongxuan, Kang, Yue, Lee, Thomas C. M.
Format: Preprint
Published: 2025
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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