The online meta-learning framework is designed for the continual lifelong learning setting. It bridges two fields: meta-learning which tries to extract prior knowledge from past tasks for fast learning of future tasks, and online-learning which tackles the sequential setting where problems are revealed one by one. In this paper, we generalize the original framework from convex to non-convex setting, and introduce the local regret as the alternative performance measure. We then apply this framework to stochastic settings, and show theoretically that it enjoys a logarithmic local regret, and is robust to any hyperparameter initialization. The empirical test on a real-world task demonstrates its superiority compared with traditional methods.