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.