Meta Mirror Descent: Optimiser Learning for Fast Convergence

• URL: http://arxiv.org/abs/2203.02711v1
• Date: Sat, 5 Mar 2022 11:41:13 GMT
• Title: Meta Mirror Descent: Optimiser Learning for Fast Convergence
• Authors: Boyan Gao, Henry Gouk, Hae Beom Lee, Timothy M. Hospedales
• Abstract summary: 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. Unlike many meta-learned optimisers, it also supports convergence and generalisation guarantees and uniquely does so without requiring validation data.
• Score: 85.98034682899855
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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