Accurate Sample Complexity Bounds for Multitask and Meta-Learning

In this paper, we explore the problem of learning multiple tasks simultaneously, known as multitask learning or metalearning. We discuss how to efficiently learn a representation that can be specialized for each task using fewer samples than would be needed to learn each task individually. Our approach reduces the sample complexity by leveraging shared structure across tasks, which is particularly useful when there are too few samples per task to learn an accurate classifier on their own.
We compare our method to other approaches that rely on model-agnostic metalearning (MAML) or PAC-Bayes bounds for multitask and metalearning. While these works consider more restrictive settings than ours, they typically focus on studying practical heuristics such as MAML rather than the optimal sample complexity of learning specific families of tasks.
To better understand the efficiency of our approach, imagine you have a big box full of different objects, each with its own unique features and properties. In multitask learning, we want to find a way to represent these objects in a compact and efficient manner, so we can quickly identify them without having to examine each one individually. By sharing information across objects, we can create a more accurate representation that requires fewer samples than if we were to learn each object separately.
Our results show that our method reduces the sample complexity considerably compared to previous upper bounds, even in the agnostic setting. We also demonstrate that computationally efficient algorithms can be used to solve these tasks efficiently.
In summary, this paper presents a new approach to multitask learning that leverages shared structure across tasks to reduce the sample complexity of learning a representation for each task. Our method has important implications for improving the efficiency of machine learning algorithms in a wide range of applications.