  This paper focuses on online kernel learning over a decentralized network.
Each agent in the network receives continuous streaming data locally and works
collaboratively to learn a nonlinear prediction function that is globally
optimal in the reproducing kernel Hilbert space with respect to the total
instantaneous costs of all agents. In order to circumvent the curse of
dimensionality issue in traditional online kernel learning, we utilize random
feature (RF) mapping to convert the non-parametric kernel learning problem into
a fixed-length parametric one in the RF space. We then propose a novel learning
framework named Online Decentralized Kernel learning via Linearized ADMM
(ODKLA) to efficiently solve the online decentralized kernel learning problem.
To further improve the communication efficiency, we add the quantization and
censoring strategies in the communication stage and develop the Quantized and
Communication-censored ODKLA (QC-ODKLA) algorithm. We theoretically prove that
both ODKLA and QC-ODKLA can achieve the optimal sublinear regret
$\mathcal{O}(\sqrt{T})$ over $T$ time slots. Through numerical experiments, we
evaluate the learning effectiveness, communication, and computation
efficiencies of the proposed methods.
