# Dynamic Regret Analysis for Online Meta-Learning

arXiv: https://arxiv.org/abs/2109.14375 · HTML: https://mlsanity.com/paper/2109.14375/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 29 Sep 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [Online Meta-Learning](https://mlsanity.com/paper/1902.08438/) (2019)
- [Continuous Adaptation via Meta-Learning in Nonstationary and Competitive Environments](https://mlsanity.com/paper/1710.03641/) (2017)
- [Tight Analyses for Non-Smooth Stochastic Gradient Descent](https://mlsanity.com/paper/1812.05217/) (2018)
- [A High Probability Analysis of Adaptive SGD with Momentum](https://mlsanity.com/paper/2007.14294/) (2020)
- [Learning-to-Learn Stochastic Gradient Descent with Biased Regularization](https://mlsanity.com/paper/1903.10399/) (2019)
- [DADAM: A Consensus-based Distributed Adaptive Gradient Method for Online Optimization](https://mlsanity.com/paper/1901.09109/) (2019)
- [Efficient Regret Minimization in Non-Convex Games](https://mlsanity.com/paper/1708.00075/) (2017)
- [Dynamic Local Regret for Non-convex Online Forecasting](https://mlsanity.com/paper/1910.07927/) (2019)
- [No-regret Non-convex Online Meta-Learning](https://mlsanity.com/paper/1910.10196/) (2019)
- [Adaptive First-and Zeroth-order Methods for Weakly Convex Stochastic Optimization Problems](https://mlsanity.com/paper/2005.09261/) (2020)
- [Meta-ViterbiNet: Online Meta-Learned Viterbi Equalization for Non-Stationary Channels](https://mlsanity.com/paper/2103.13483/) (2021)
- [Online Optimization in Dynamic Environments](https://mlsanity.com/paper/1307.5944/) (2013)
- [Task-Robust Model-Agnostic Meta-Learning](https://mlsanity.com/paper/2002.04766/) (2020)
- [Double Meta-Learning for Data Efficient Policy Optimization in Non-Stationary Environments](https://mlsanity.com/paper/2011.10714/) (2020)

## Built on by (most cited first, 4 of 4)

- [Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods](https://mlsanity.com/paper/2207.02829/) (2022)
- [Non-Convex Bilevel Optimization with Time-Varying Objective Functions](https://mlsanity.com/paper/2308.03811/) (2023)
- [Dynamic Regret of Adaptive Gradient Methods for Strongly Convex Problems](https://mlsanity.com/paper/2209.01608/) (2022)
- [To Retain or to Adapt? Generalizing Continual Learning](https://mlsanity.com/paper/2607.05609/) (2026)

## Abstract (arXiv)

The online meta-learning framework has arisen as a powerful tool for the continual lifelong learning setting. The goal for an agent is to quickly learn new tasks by drawing on prior experience, while it faces with tasks one after another. This formulation involves two levels: outer level which learns meta-learners and inner level which learns task-specific models, with only a small amount of data from the current task. While existing methods provide static regret analysis for the online meta-learning framework, we establish performance in terms of dynamic regret which handles changing environments from a global prospective. We also build off of a generalized version of the adaptive gradient methods that covers both ADAM and ADAGRAD to learn meta-learners in the outer level. We carry out our analyses in a stochastic setting, and in expectation prove a logarithmic local dynamic regret which depends explicitly on the total number of iterations T and parameters of the learner. Apart from, we also indicate high probability bounds on the convergence rates of proposed algorithm with appropriate selection of parameters, which have not been argued before.