摘要：Data are increasingly distributed across networked agents that must learn collaboratively without exchanging raw observations or relying on central coordination. Existing decentralized methods largely focus on finite-dimensional models with smooth and strongly convex objectives, leaving nonparametric distributional learning over networks underexplored. We study decentralized nonparametric quantile regression in reproducing kernel Hilbert spaces. The standard kernel estimator is poorly suited to this setting: the check loss is nonsmooth, while its representer theorem formulation requires a global, data dependent basis whose dimension grows with the total sample size. We reformulate the estimator using convolution smoothing and shared random features, yielding a differentiable objective with a common, data-independent parameterization of substantially lower dimension. We develop a gradient-adjusted alternating direction method of multipliers algorithm that replaces costly local minimization with network corrected gradient updates, together with a communication-enhanced variant that selectively transmits updates. We establish nonasymptotic error bounds for the smoothed full-kernel and random-feature estimators, showing that the latter attains the full-kernel rate with suitable bandwidth and feature dimension. We also show both algorithms converge linearly to the random-feature consensus estimator. Simulations and a real data application demonstrate competitive predictive accuracy with substantial computational and communication savings.

 

Bio: 常晋源，西南财经大学光华首席教授、中国科学院数学与系统科学研究院研究员，主要从事大规模复杂数据分析相关的研究，先后担任统计学、计量经济学和运筹优化国际学术期刊Statistica Sinica、Journal of the Royal Statistical Society Series B、Journal of Business & Economic Statistics、Journal of the American Statistical Association和Operations Research的副主编，获得过国务院政府特殊津贴、霍英东教育基金会高等院校青年科学奖一等奖和青年教师奖一等奖、教育部高等学校科学研究优秀成果奖、四川省青年科技奖等奖励，获四川省基础研究领衔科学家专项资助。