On Weight-Sharing and Bilevel Optimization in Architecture Search

Sep 25, 2019 Blind Submission readers: everyone Show Bibtex
  • TL;DR: An analysis of the learning and optimization structures of architecture search in neural networks and beyond.
  • Abstract: Weight-sharing—the simultaneous optimization of multiple neural networks using the same parameters—has emerged as a key component of state-of-the-art neural architecture search. However, its success is poorly understood and often found to be surprising. We argue that, rather than just being an optimization trick, the weight-sharing approach is induced by the relaxation of a structured hypothesis space, and introduces new algorithmic and theoretical challenges as well as applications beyond neural architecture search. Algorithmically, we show how the geometry of ERM for weight-sharing requires greater care when designing gradient- based minimization methods and apply tools from non-convex non-Euclidean optimization to give general-purpose algorithms that adapt to the underlying structure. We further analyze the learning-theoretic behavior of the bilevel optimization solved by practical weight-sharing methods. Next, using kernel configuration and NLP feature selection as case studies, we demonstrate how weight-sharing applies to the architecture search generalization of NAS and effectively optimizes the resulting bilevel objective. Finally, we use our optimization analysis to develop a simple exponentiated gradient method for NAS that aligns with the underlying optimization geometry and matches state-of-the-art approaches on CIFAR-10.
  • Keywords: neural architecture search, weight-sharing, bilevel optimization, non-convex optimization, hyperparameter optimization, model selection
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