New Tight Relaxations of Rank Minimization for Multi-Task Learning

Wei Chang; Feiping Nie; Rong Wang; Xuelong Li

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arXiv · 2112.04734

New Tight Relaxations of Rank Minimization for Multi-Task Learning

Wei Chang·Feiping Nie·Rong Wang·Xuelong Li

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Abstract

Multi-task learning has been observed by many researchers, which supposes that different tasks can share a low-rank common yet latent subspace. It means learning multiple tasks jointly is better than learning them independently. In this paper, we propose two novel multi-task learning formulations based on two regularization terms, which can learn the optimal shared latent subspace by minimizing the exactly $k$ minimal singular values. The proposed regularization terms are the more tight approximations of rank minimization than trace norm. But it's an NP-hard problem to solve the exact rank minimization problem. Therefore, we design a novel re-weighted based iterative strategy to solve our models, which can tactically handle the exact rank minimization problem by setting a large penalizing parameter. Experimental results on benchmark datasets demonstrate that our methods can correctly recover the low-rank structure shared across tasks, and outperform related multi-task learning methods.

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Wei Chang, Feiping Nie, Rong Wang, Xuelong Li. 2021-12-09. New Tight Relaxations of Rank Minimization for Multi-Task Learning. https://arxiv.org/abs/2112.04734

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