带记忆的广义线性老虎机
Generalized Linear Bandits with Memory
浏览论文内容
中文总结 AI 辅助
该研究针对带记忆的广义线性老虎机，改进了线性情况下的遗憾界，提出基于收缩置信界的分块算法，实现了$\text{sqrt}(T)$型遗憾率，通过数值实验验证了理论结果。
中文摘要 AI 辅助
我们研究带记忆的广义线性老虎机，这是一种内生非平稳设置，其中奖励通过有限记忆矩阵依赖于过去的动作。基于线性模型的现有工作（Clerici等人，2024），我们表明先前已知的$\tilde{O}(T^{3/4})$遗憾界源于宽松的分析，我们提供了更精确的分析，在线性情况下恢复了$\tilde{O}(\text{sqrt}(T))$的遗憾率。然后我们将这一改进扩展到广义线性模型，并提出了一种基于收缩置信界的分块算法。我们的算法实现了$\tilde{O}(\text{sqrt}(mT) + d\text{sqrt}(T) + \text{sqrt}(\text{κ}) d^{2} m^{1/4} T^{1/4} + \text{κ} d^{2})$的遗憾界，其中$d$表示特征维度，$m$表示记忆长度，$\text{κ}$表示链接函数的曲率参数。尽管存在非线性奖励和记忆效应，该算法仍达到了$\text{sqrt}(T)$型的速率。据我们所知，该分析提供了对记忆诱导的非平稳性和非线性链接函数的统一处理，同时确保主导遗憾项独立于链接函数的曲率。我们进行了与理论发现一致的数值实验。
英文摘要
We study generalized linear bandits with memory, an endogenous non-stationary setting in which rewards depend on past actions through a finite memory matrix. Building on prior work for linear models (Clerici et al., 2024), we show that the previously known $\tilde{O}(T^{3/4})$ regret bound stems from a loose analysis, and we provide a sharpened analysis that recovers a $\tilde{O}(\sqrt{T})$ regret rate in the linear case. We then extend this improvement to generalized linear models and propose a block-wise algorithm based on shrunken confidence bounds. Our algorithm achieves a regret bound of $\tilde{O}\left(\sqrt{mT} + d\sqrt{T} + \sqrtκ\, d^{2} m^{1/4} T^{1/4} + κd^{2} \right)$, where $d$ denotes the feature dimension, $m$ the memory length, and $κ$ a curvature parameter of the link function. This attains a $\sqrt{T}$-type rate despite nonlinear rewards and memory effects. To the best of our knowledge, this analysis provides a unified treatment of memory-induced non-stationarity and nonlinear link functions, while ensuring that the leading regret term is independent of the curvature of the link function. We conduct numerical experiments that are consistent with our theoretical findings.
发表机构
- Seoul National University（首尔大学）
- Shinsegae（新世界（集团））
机构由 AI 辅助整理，请以论文原文为准。
