Optimistic Meta-Gradients

Sebastian Flennerhag, Tom Zahavy, Brendan O'Donoghue, Hado van Hasselt, András György, Satinder Singh

Keywords: meta-learning, online optimisation, convex optimisation

TL;DR: We study the connection between gradient-based (online) meta-learning and convex optimisation in the single task setting.

Abstract:

We study the connection between gradient-based meta-learning and convex optimisation. 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 the recently proposed Bootstrapped Meta-Gradient (Flennerhag et. al., 2022) method, providing deeper insight into its underlying mechanics.

Submission Number: 13481