Optimistic Meta-Gradients

TL;DR

This paper explores the theoretical connections between gradient-based meta-learning and convex optimization, revealing that optimism is essential for acceleration and introducing Bootstrapped Meta-Gradients for capturing this optimism.

Contribution

It establishes convergence rates for meta-learning, shows the necessity of optimism for acceleration, and links meta-gradients with optimization theory.

Findings

Gradient descent with momentum is a special case of meta-gradients.

Meta-learned updates can improve convergence speed but do not accelerate without optimism.

Bootstrapped Meta-Gradients effectively capture optimism in meta-learning.

Abstract

We study the connection between gradient-based meta-learning and convex op-timisation. We observe that gradient descent with momentum is a special case of meta-gradients, and building on recent results in optimisation, we prove convergence rates for meta-learning in the single task setting. While a meta-learned update rule can yield faster convergence up to constant factor, it is not sufficient for acceleration. Instead, some form of optimism is required. We show that optimism in meta-learning can be captured through Bootstrapped Meta-Gradients (Flennerhag et al., 2022), providing deeper insight into its underlying mechanics.