Title: MetaMD: Principled Optimiser Meta-Learning for Deep Learning. Abstract: Optimiser design influences learning speed and generalisation in training machine learning models. Several studies have attempted to learn more effective gradient-descent optimisers via solving a bi-level optimisation problem where generalisation error is minimised with respect to optimiser parameters. However, most existing neural network oriented optimiser learning methods are intuitively motivated, without clear theoretical support, and focus on learning implicit biases that improve generalisation, rather than speed of convergence. We take a different perspective starting from mirror descent rather than gradient descent, and meta-learning the corresponding Bregman divergence. Within this paradigm, we formalise a novel meta-learning objective of optimising the rate of convergence. The resulting framework, termed Meta Mirror Descent (MetaMD), learns to accelerate optimisation speed. Unlike many meta-learned neural network optimisers, it also supports convergence guarantees and uniquely does so without requiring validation data. We empirically evaluate our framework on a variety of tasks and architectures in terms of convergence rate and generalisation error and demonstrate strong performance.