Given a finite set of sample points, meta-learning algorithms aim to learn an optimal adaptation strategy for new, unseen tasks. Often, this data can be ambiguous as it might belong to different tasks concurrently. This is particularly the case in meta-regression tasks. In such cases, the estimated adaptation strategy is subject to high variance due to the limited amount of support data for each task, which often leads to sub-optimal generalization performance. In this work, we address the problem of variance reduction in gradient-based meta-learning and formalize the class of problems prone to this, a condition we refer to as \emph{task overlap}. Specifically, we propose a novel approach that reduces the variance of the gradient estimate by weighing each support point individually by the variance of its posterior over the parameters. To estimate the posterior, we utilize the Laplace approximation, which allows us to express the variance in terms of the curvature of the loss landscape of our meta-learner. Experimental results demonstrate the effectiveness of the proposed method and highlight the importance of variance reduction in meta-learning.

本研究针对元学习中的高方差问题，尤其是在元回归任务中的任务重叠现象进行探讨。提出了一种新方法，通过拉普拉斯近似对每个支持点的后验方差进行加权，从而减少梯度估计的方差。实验结果表明，方差的减少显著提高了元学习的泛化性能。

通过拉普拉斯近似减少元学习中回归任务的方差