Keywords: active learning, representation learning, robotics, theory
Abstract: 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 \emph{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%.
Supplementary Material: pdf
Submission Number: 8623
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