Optimistic Meta-Gradients
This work offers theoretical insights into meta-learning optimization, but it is incremental as it builds on existing results to analyze convergence without introducing a new paradigm.
The paper connects gradient-based meta-learning to convex optimization, showing that meta-learned update rules can improve convergence speed by a constant factor but require optimism for acceleration, with Bootstrapped Meta-Gradients providing a framework to understand this mechanism.
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.