Optimistic Meta-Gradients

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.

Authors

• Sebastian Flennerhag
• Tom Zahavy
• Brendan O'Donoghue
• Hado P. van Hasselt
• András György
• Satinder Singh

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