Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for \textit{active representation learning}, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve $\varepsilon$-excess risk on target scales with $ (k^*)^2 \|v^*\|_2^2 \varepsilon^{-2}$ where $k^*$ is the effective dimension of the target and $\|v^*\|_2^2 \in (0,1]$ represents the connection between source and target space. Compared to the passive one, this can save up to $\frac{1}{d_W}$ of sample complexity, where $d_W$ is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by $20\%-70\%$.

本文提出了一种基于多任务预训练的表示学习的算法和理论框架，称之为主动表示学习，它通过从一组源任务中抽取数据来学习针对特定目标任务的最佳表示，同时兼容深度表示学习实践，旨在提高样本利用率。

机器人学中的一般任务空间主动表示学习应用