ML has been increasingly adopted in wireless communications, with popular techniques, such as supervised, unsupervised, and reinforcement learning, applied to traffic classification, channel encoding/ decoding, and cognitive radio. This article discusses a different class of ML technique, stochastic online learning, and its promising applications to MEC. Based on stochastic gradient descent, stochastic online learning learns from the changes of dynamic systems (i.e., the gradient of the Lagrange multipliers) rather than training data, decouples tasks between time slots and edge devices, and asymptotically minimizes the time-averaged operational cost of MEC in a fully distributed fashion with the increase of the learning time. By taking the widely adopted big data analytic framework MapReduce as an example, numerical studies show that the network throughput can increase by eight times through adopting stochastic online learning as compared to existing offline implementations.