Momentum LMS Theory beyond Stationarity: Stability, Tracking, and Regret
School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences（中国科学院大学先进交叉学科学院）；State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学科学国家重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
In large-scale data processing scenarios, data often arrive in sequential streams generated by complex systems that exhibit drifting distributions and time-varying system parameters. This nonstationarity challenges theoretical analysis, as it violates classical assumptions of i.i.d. (independent and identically distributed) samples, necessitating algorithms capable of real-time updates without expensive retraining. An effective approach should process each sample in a single pass, while maintaining computational and memory complexities independent of the data stream length. Motivated by these challenges, this paper investigates the Momentum Least Mean Squares (MLMS) algorithm as an adaptive identification tool, leveraging its computational simplicity and online processing capabilities. Theoretically, we derive tracking performance and regret bounds for the MLMS in time-varying stochastic linear systems under various practical conditions. Unlike classical LMS, whose stability can be characterized by first-order random vector difference equations, MLMS introduces an additional dynamical state due to momentum, leading to second-order time-varying random vector difference equations whose stability analysis hinges on more complicated products of random matrices, which poses a substantially challenging problem to resolve. Experiments on synthetic and real-world data streams demonstrate that MLMS achieves rapid adaptation and robust tracking, in agreement with our theoretical results especially in nonstationary settings, highlighting its promise for modern streaming and online learning applications.
Online Optimization of Difference-of-Convex Compositions with Smooth Mappings
Management Science and Engineering, Stanford University（斯坦福大学管理科学与工程系）；The Daniel J. Epstein Department of Industrial and Systems Engineering, University of Southern California（南加州大学丹尼尔·J·埃普斯坦工业与系统工程系）
Improved Analysis for Dynamic Regret of Strongly Convex and Smooth Functions
National Key Laboratory for Novel Software Technology（计算机软件新技术国家重点实验室）；Nanjing University（南京大学）
本文对强凸光滑函数的动态后悔问题提出了一种改进的分析方法。具体来说，我们研究了Zhang et al.（2017）提出的在线多梯度下降（OMGD）算法。原始的分析表明，OMGD的动态遗憾最多是$\mathcal{O}(\min\{\mathcal{P}_T,\mathcal{S}_T\})$，其中$\mathcal{P}_T$和$\mathcal{S}_T$是路径长度和平方路径长度，测量的在线功能的最小值的累积移动。我们证明，通过改进的分析，OMGD的动态遗憾可以改进为$\mathcal{O}(\min\{\mathcal{P}_T,\mathcal{S}_T,\mathcal{V}_T\})$，其中$\mathcal{V}_T$是在线函数的函数变化。请注意，$\mathcal{P}_T, \mathcal{S}_T, \mathcal{V}_T$的数量本质上反映了环境非平稳性的不同方面--它们通常不具有可比性，并且在不同的情况下更受欢迎。因此，本文提出的动态后悔实际上实现了\emph{best-of-three-worlds}保证，并且比以前的结果严格。
Regret Bounds for Generalized Linear Bandits under Parameter Drift
LTCI；TélécomParis（巴黎电信学院）；ENS Paris（巴黎高等师范学院）；Université PSL（巴黎文理大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；Criteo AI Lab（Criteo人工智能实验室）；Criteo（Criteo公司）
Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles
Center for Computational Science and Engineering, MIT（麻省理工学院计算科学与工程中心）；Department of Civil and Environmental Engineering, MIT（麻省理工学院土木与环境工程系）；Institute for Data, Systems, and Society, MIT（麻省理工学院数据、系统与社会研究所）
Non-Stationary Online Structured Prediction with Surrogate Losses
CyberAgent, Tokyo, Japan（日本东京CyberAgent公司）；National Institute of Informatics, Tokyo, Japan（日本东京信息机构）；Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan（日本东京RIKEN高级智能项目）；The Institute of Statistical Mathematics, Tokyo, Japan（日本东京统计数学研究所）；Tohoku University, Miyagi, Japan（日本宫城县立东大学）；Nanyang Technological University, Singapore（新加坡南洋理工大学）
From Theory to Practice with RAVEN-UCB: Addressing Non-Stationarity in Multi-Armed Bandits through Variance Adaptation
School of Business, Central South University（中南大学商学院）；School of Finance and Statistics, Hunan University（湖南大学金融与统计学院）；Wisdom Lake Academy of Pharmacy, Xi’an Jiaotong-Liverpool University（西安交通大学利物浦大学智慧湖药学院）
Decentralized Online Regularized Learning Over Random Time-Varying Graphs
East China Normal University（华东师范大学）；No.2 High School of East China Normal University（华东师范大学第二附属中学）；Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院系统科学研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Ningbo University（宁波大学）
