# Meta Learning in the Continuous Time Limit

arXiv: https://arxiv.org/abs/2006.10921 · HTML: https://mlsanity.com/paper/2006.10921/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [Bridging Multi-Task Learning and Meta-Learning: Towards Efficient Training and Effective Adaptation](https://mlsanity.com/paper/2106.09017/) (2021)
- [Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2111.03947/) (2021)
- [Generalization of Model-Agnostic Meta-Learning Algorithms: Recurring and Unseen Tasks](https://mlsanity.com/paper/2102.03832/) (2021)
- [Global Convergence of MAML and Theory-Inspired Neural Architecture Search for Few-Shot Learning](https://mlsanity.com/paper/2203.09137/) (2022)
- [Learn to Match with No Regret: Reinforcement Learning in Markov Matching Markets](https://mlsanity.com/paper/2203.03684/) (2022)
- [Continuous-Time Meta-Learning with Forward Mode Differentiation](https://mlsanity.com/paper/2203.01443/) (2022)
- [Meta-Learning with Adjoint Methods](https://mlsanity.com/paper/2110.08432/) (2021)
- [Finding Regularized Competitive Equilibria of Heterogeneous Agent Macroeconomic Models with Reinforcement Learning](https://mlsanity.com/paper/2303.04833/) (2023)
- [Cascaded Gaps: Towards Gap-Dependent Regret for Risk-Sensitive Reinforcement Learning](https://mlsanity.com/paper/2203.03110/) (2022)
- [Taming Equilibrium Bias in Risk-Sensitive Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2405.02724/) (2024)

## Abstract (arXiv)

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.