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Utilizing task-invariant prior knowledge extracted from related tasks,meta-learning is a principled framework that empowers learning a new taskespecially when data records are limited. A fundamental challenge inmeta-learning is how to quickly "adapt" the extracted prior in order to train atask-specific model within a few optimization steps. Existing approaches dealwith this challenge using a preconditioner that enhances convergence of theper-task training process. Though effective in representing locally a quadratictraining loss, these simple linear preconditioners can hardly capture complexloss geometries. The present contribution addresses this limitation by learninga nonlinear mirror map, which induces a versatile distance metric to enablecapturing and optimizing a wide range of loss geometries, hence facilitatingthe per-task training. Numerical tests on few-shot learning datasetsdemonstrate the superior expressiveness and convergence of the advocatedapproach.

Meta-Learning with Versatile Loss Geometries for Fast Adaptation Using Mirror Descent