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arXiv 2410.04080cs.LG
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跨学习上下文赌博机在未知上下文分布下的高概率界

High Probability Bound for Cross-Learning Contextual Bandits with Unknown Context Distributions

School of Data Science Fudan University(复旦大学数据科学学院)

Ruiyuan Huang, Zengfeng Huang

AI总结:

针对上下文分布未知的跨学习上下文赌博机问题,本文深入分析现有算法,利用时期间弱依赖结构并改进鞅不等式,证明其以高概率实现近乎最优遗憾。

摘要:

受在线竞价和休眠赌博机应用的启发,我们研究了具有跨学习的上下文赌博机问题,其中学习者观察到与所有可能上下文相关的动作损失,而不仅仅是当前轮次的上下文。我们关注的是损失由对手选择、上下文从特定分布中独立同分布采样的设置。该问题最早由Balseiro等人(2019)研究,他们提出了一种在假设上下文分布预先已知的情况下实现近乎最优遗憾的算法。然而,这一假设往往不切实际。为解决此问题,Schneider和Zimmert(2023)最近提出了一种实现近乎最优期望遗憾的新算法。众所周知,期望遗憾可能明显弱于高概率界。在本文中,我们对其算法进行了新颖而深入的分析,并证明该算法实际上以高概率实现近乎最优遗憾。Schneider和Zimmert(2023)的原始分析中有一些步骤本质上只能得出期望界。在我们的分析中,我们引入了若干新见解。具体而言,我们广泛利用了不同时期之间的弱依赖结构,这在以往的分析中被忽视。此外,标准鞅不等式不能直接适用,因此我们改进了鞅不等式以完成我们的分析。

英文摘要:

Motivated by applications in online bidding and sleeping bandits, we examine the problem of contextual bandits with cross learning, where the learner observes the loss associated with the action across all possible contexts, not just the current round's context. Our focus is on a setting where losses are chosen adversarially, and contexts are sampled i.i.d. from a specific distribution. This problem was first studied by Balseiro et al. (2019), who proposed an algorithm that achieves near-optimal regret under the assumption that the context distribution is known in advance. However, this assumption is often unrealistic. To address this issue, Schneider and Zimmert (2023) recently proposed a new algorithm that achieves nearly optimal expected regret. It is well-known that expected regret can be significantly weaker than high-probability bounds. In this paper, we present a novel, in-depth analysis of their algorithm and demonstrate that it actually achieves near-optimal regret with high probability. There are steps in the original analysis by Schneider and Zimmert (2023) that lead only to an expected bound by nature. In our analysis, we introduce several new insights. Specifically, we make extensive use of the weak dependency structure between different epochs, which was overlooked in previous analyses. Additionally, standard martingale inequalities are not directly applicable, so we refine martingale inequalities to complete our analysis.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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