  In this paper, we establish the ordinary differential equation (ODE) that
underlies the training dynamics of Model-Agnostic Meta-Learning (MAML). Our
continuous-time limit view of the process eliminates the influence of the
manually chosen step size of gradient descent and includes the existing
gradient descent training algorithm as a special case that results from a
specific discretization. We show that the MAML ODE enjoys a linear convergence
rate to an approximate stationary point of the MAML loss function for strongly
convex task losses, even when the corresponding MAML loss is non-convex.
Moreover, through the analysis of the MAML ODE, we propose a new BI-MAML
training algorithm that significantly reduces the computational burden
associated with existing MAML training methods. To complement our theoretical
findings, we perform empirical experiments to showcase the superiority of our
proposed methods with respect to the existing work.
