发表机构
School of Mathematics, Nanjing University; School of Artificial Intelligence, Nanjing University, National Key Laboratory for Novel Software Technology; School of Mathematics and Physics, Xi’an Jiaotong-Liverpool University（南京大学数学系; 南京大学人工智能学院，计算机软件新技术国家重点实验室; 西交利物浦大学数理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究重尾噪声下广义线性带式赌博机问题，基于在线镜像下降方法提出算法EHM，实现几乎最优遗憾值且无需常用参数，还研究了上下文特征分段常数时的情况及非线性带式赌博机特殊情况，给出相应算法并证明遗憾上界。
AI 中文摘要
本文首先研究重尾噪声下的广义线性带式赌博机（GLB）问题。重尾分布特征在个性化推荐、金融市场和医疗等实际应用中广泛存在。基于在线镜像下降（OMD）方法，我们提出算法EHM，它扩展了自适应Huber损失方法，实现几乎最优遗憾值$\widetilde{\mathcal{O}}(T^{\frac{1}{1+\epsilon}})$，且无需常用参数。接着研究上下文特征分段常数时的GLB问题，得到PGLB - EHM算法，遗憾上界阶不变。还深入研究非线性带式赌博机特殊情况，给出NB - EHM算法，最终利用仿射提升方法表明一般NB问题可用NB - EHM实现次线性遗憾界。
英文摘要
In this paper we first study the problem of generalized linear bandit (GLB) under heavy-tailed noise. The characteristics of heavy-tailed distributions are widely observed in real-world applications such as personalized recommendation, financial markets, and medical treatments. Based on the online mirror descent (OMD) method, we propose an algorithm EHM that extends the adaptive Huber loss method (Wang et al., 2025) with one-pass update ($\mathcal{O}(1)$ computational complexity with respect to current round $t$ and the time horizon $T$), which simultaneously achieves an almost optimal regret of $\widetilde{\mathcal{O}}(T^{\frac{1}{1+ε}})$ where $T$ is the time horizon. In addition, by utilizing a special property of some link function (Sawarni et al., 2025), our algorithm eliminates the need to know a commonly used parameter. Next, we study the GLB problem under the case when contextual characteristic becomes piecewise constant, and we slightly revised former algorithm to obtain the PGLB-EHM algorithm. After theoretical analysis, we prove that the regret upper bound order stays the same. Furthermore, we look deeper into a special case of nonlinear bandit (NB) and present the NB-EHM algorithm with bisection method and special restriction. Eventually we utilize the affine lifting approach and show that the general NB problem can be applied with NB-EHM to achieve a sublinear regret bound.
