Meta-Learning with Versatile Loss Geometries for Fast Adaptation Using Mirror Descent
This work addresses a bottleneck in meta-learning for fast adaptation in data-limited scenarios, offering an incremental improvement over linear preconditioners.
The paper tackles the challenge of capturing complex loss geometries in meta-learning by learning a nonlinear mirror map, which improves per-task training convergence. Numerical tests on few-shot learning datasets show superior expressiveness and convergence compared to existing methods.
Utilizing task-invariant prior knowledge extracted from related tasks, meta-learning is a principled framework that empowers learning a new task especially when data records are limited. A fundamental challenge in meta-learning is how to quickly "adapt" the extracted prior in order to train a task-specific model within a few optimization steps. Existing approaches deal with this challenge using a preconditioner that enhances convergence of the per-task training process. Though effective in representing locally a quadratic training loss, these simple linear preconditioners can hardly capture complex loss geometries. The present contribution addresses this limitation by learning a nonlinear mirror map, which induces a versatile distance metric to enable capturing and optimizing a wide range of loss geometries, hence facilitating the per-task training. Numerical tests on few-shot learning datasets demonstrate the superior expressiveness and convergence of the advocated approach.