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.

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