Active Representation Learning for General Task Space with Applications in Robotics

• URL: http://arxiv.org/abs/2306.08942v1
• Date: Thu, 15 Jun 2023 08:27:50 GMT
• Title: Active Representation Learning for General Task Space with Applications in Robotics
• Authors: Yifang Chen, Yingbing Huang, Simon S. Du, Kevin Jamieson, Guanya Shi
• Abstract summary: We propose an algorithmic framework for textitactive representation learning, where the learner optimally chooses which source tasks to sample from. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. Our algorithms outperform baselines by $20%-70%$ on average.
• Score: 44.36398212117328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \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 $20\%-70\%$.

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