Dynamic Regret Analysis for Online Meta-Learning

TL;DR

This paper introduces a dynamic regret analysis for online meta-learning, providing theoretical guarantees for adapting to changing environments and extending adaptive gradient methods like ADAM and ADAGRAD.

Contribution

It establishes the first dynamic regret bounds for online meta-learning and extends adaptive gradient methods to this setting with probabilistic convergence guarantees.

Findings

Logarithmic local dynamic regret bound in expectation

High probability convergence bounds for the proposed algorithm

Extension of adaptive gradient methods to meta-learning context

Abstract

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.