Task-similarity Aware Meta-learning through Nonparametric Kernel Regression
Authors: Arun Venkitaraman, Anders Hansson, Bo Wahlberg
Keywords: Task-similarity, Meta-learning, Kernel regression, Nonparametric regression, Task-descriptors
Abstract: This paper investigates the use of nonparametric kernel-regression to obtain a task- similarity aware meta-learning algorithm. Our hypothesis is that the use of task- similarity helps meta-learning when the available tasks are limited and may contain outlier/ dissimilar tasks. While existing meta-learning approaches implicitly assume the tasks as being similar, it is generally unclear how this task-similarity could be quantified and used in the learning. As a result, most popular meta- learning approaches do not actively use the similarity/dissimilarity between the tasks, but rely on availability of huge number of tasks for their working. Our contribution is a novel framework for meta-learning that explicitly uses task-similarity in the form of kernels and an associated meta-learning algorithm. We model the task-specific parameters to belong to a reproducing kernel Hilbert space where the kernel function captures the similarity across tasks. The proposed algorithm iteratively learns a meta-parameter which is used to assign a task-specific descriptor for every task. The task descriptors are then used to quantify the task-similarity through the kernel function. We show how our approach conceptually generalizes the popular meta-learning approaches of model-agnostic meta-learning (MAML) and Meta-stochastic gradient descent (Meta-SGD) approaches. Numerical experiments with regression and classification tasks show that our algorithm outperforms these approaches when the number of tasks is limited, even in the presence of out- lier or dissimilar tasks. This supports our hypothesis that task-similarity helps improve the meta-learning performance in task-limited and adverse settings.