Model-Agnostic Meta-Learning using Runge-Kutta Methods

Daniel Jiwoong Im 1, Yibo Jiang 2, and Nakul Verma 3 1 Janelia Research Campus, HHMI, Virgina 2 Harvard University, Massachusetts 3 Columbia University, New York Abstract Meta learning has emerged as an important framework for learning new tasks from just a few examples. The success of any meta-learning model depends on (i) its fast adaptation to new tasks, as well as (ii) having a shared representation across similar tasks. Here we extend the model-agnostic meta-learning (MAML) framework introduced by Finn et al. (2017) to achieve improved performance by analyzing the temporal dynamics of the optimization procedure via the Runge-Kutta method. This method enables us to gain fine-grained control over the optimization and helps us achieve both the adaptation and representation goals across tasks. By leveraging this refined control, we demonstrate that there are multiple principled ways to update MAML and show that the classic MAML optimization is simply a special case of second order Runge-Kutta method that mainly focuses on fast-adaptation. Experiments on benchmark classification, regression and reinforcement learning tasks show that this refined control helps attain improved results. 1 Introduction Building an intelligent system that can learn quickly on a new task with few examples or few experiences is one of the central goals of machine learning. Achieving this goal requires an agent that learns continuously while having the ability to adapt to new tasks with limited data. Meta-learning (Biggs, 1985) has emerged as a compelling framework that strives to attain this challenging goal. There are two main approaches to meta-learning: learning-to-optimize and learning-to-initialize the meta-model (usually encoded as deep network).