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Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.
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Meta-Learning Priors Using Unrolled Proximal Networks
Relying on prior knowledge accumulated from related tasks, meta-learning offers a powerful approach to learning a novel task from a limited number of training data. Recent approaches use a family of prior probability density functions or recurrent neural network models, whose parameters can be optimized by utilizing labeled data from the observed tasks. While these approaches have appealing empirical performance, expressiveness of their prior is relatively low, which limits generalization and interpretation of meta-learning. Aiming at expressive yet meaningful priors, this contribution puts forth a novel prior representation model that leverages the notion of algorithm unrolling. The key idea is to unroll the proximal gradient descent steps, where learnable piecewise linear functions are developed to approximate the desired proximal operators within tight theoretical error bounds established for both smooth and non-smooth proximal functions. The resultant multi-block neural network not only broadens the scope of learnable priors, but also enhances interpretability from an optimization viewpoint. Numerical tests conducted on few-shot learning datasets demonstrate markedly improved performance with flexible, visualizable, and understandable priors.
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- Award ID(s):
- 2212318
- PAR ID:
- 10518940
- Publisher / Repository:
- International Conference of Learning Representations
- Date Published:
- Format(s):
- Medium: X
- Location:
- Vienna, Austria
- Sponsoring Org:
- National Science Foundation
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Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.more » « less
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