Improved Bilevel Model: Fast and Optimal Algorithm with Theoretical Guarantee
This work addresses the problem of inefficient bilevel optimization for researchers and practitioners, but it is incremental as it builds on existing formulations.
The paper tackles the challenge of finding an optimal formulation for bilevel programming in machine learning by proposing an improved model that converges faster and better, with empirical results showing it outperforms current models by a great margin on tasks like Data Hyper-Cleaning and Hyper Representation Learning.
Due to the hierarchical structure of many machine learning problems, bilevel programming is becoming more and more important recently, however, the complicated correlation between the inner and outer problem makes it extremely challenging to solve. Although several intuitive algorithms based on the automatic differentiation have been proposed and obtained success in some applications, not much attention has been paid to finding the optimal formulation of the bilevel model. Whether there exists a better formulation is still an open problem. In this paper, we propose an improved bilevel model which converges faster and better compared to the current formulation. We provide theoretical guarantee and evaluation results over two tasks: Data Hyper-Cleaning and Hyper Representation Learning. The empirical results show that our model outperforms the current bilevel model with a great margin. \emph{This is a concurrent work with \citet{liu2020generic} and we submitted to ICML 2020. Now we put it on the arxiv for record.}