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arXiv · 2203.02711

Meta Mirror Descent: Optimiser Learning for Fast Convergence

Boyan Gao·Henry Gouk·Hae Beom Lee·Timothy M. Hospedales
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Abstract

Optimisers are an essential component for training machine learning models, and their design influences learning speed and generalisation. 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 optimiser learning methods are intuitively motivated, without clear theoretical support. 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 minimising the regret bound of learning. The resulting framework, termed Meta Mirror Descent (MetaMD), learns to accelerate optimisation speed. Unlike many meta-learned optimisers, it also supports convergence and generalisation guarantees and uniquely does so without requiring validation data. We evaluate our framework on a variety of tasks and architectures in terms of convergence rate and generalisation error and demonstrate strong performance.

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Boyan Gao, Henry Gouk, Hae Beom Lee, Timothy M. Hospedales. 2022-03-05. Meta Mirror Descent: Optimiser Learning for Fast Convergence. https://arxiv.org/abs/2203.02711

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