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We study the connection between gradient-based meta-learning and convex optimisation. We observe that gradient descent with momentum is as 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 method, providing deeper insight into its underlying mechanics.
Author Information
Sebastian Flennerhag (DeepMind)
Ph.D. candidate in Deep Learning, focusing on network adaptation in transfer learning, meta learning and sequence learning.
Tom Zahavy (DeepMind)
Brendan O'Donoghue (DeepMind)
Hado van Hasselt (DeepMind)
András György (DeepMind)
Satinder Singh (DeepMind)
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