To enable machine learning at the edge of wireless networks (such as edge cloud), close to mobile users, is critical for future wireless networks, but challenging since the lower layers in edge cloud are substantially different from existing machine learning configurations in the cloud. In such geo-distributed computing environment, streaming data need to be evenly and cost-efficiently partitioned for different workers to produce an unbiased learning model with reduced parameter synchronization frequency. This paper presents a new online approach to optimally partitioning streaming data under time-varying network conditions. A new measure is proposed to quantify the evenness of data partitioning and restrain the optimization of data admission, partitioning, and processing. Stochastic gradient descent is applied to learn the optimal decisions online and asymptotically maximize the time-average utility of data partitioning. A new protocol is designed to further reduce the measurements of link costs, while preserving the asymptotic optimality, data evenness, and stability of the platform. Simulation results show that the proposed approach is superior to the state of the art in terms of throughput and cost efficiency, while only 24% of the links need to be measured to achieve the asymptotic optimality.