Efficient Method for Bi-level Optimization with Non-smooth Lower-Level Problem

Wanli Shi, Bin Gu

Keywords: bilevel optimization, nonsmooth

TL;DR: We propose a method solving the nonsmooth bilevel problem and give a new analysis

Abstract: Bi-level optimization plays a key role in a lot of machine learning applications. Existing state-of-the-art bi-level optimization methods are limited to smooth or some specific non-smooth lower-level problems. Therefore, achieving an efficient algorithm for the bi-level problems with a generalized non-smooth lower-level objective is still an open problem. To address this problem, in this paper, we propose a new bi-level optimization algorithm based on smoothing and penalty techniques. Using the theory of generalized directional derivative, we derive new conditions for the bilevel optimization problem with nonsmooth, perhaps non-Lipschitz lower-level problem, and prove our method can converge to the points satisfying these conditions. We also compare our method with existing state-of-the-art bi-level optimization methods and demonstrate that our method is superior to the others in terms of accuracy and efficiency.

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