Investigating Bi-Level Optimization for Learning and Vision from a Unified Perspective: A Survey and Beyond

TL;DR

This paper provides a comprehensive survey of bi-level optimization (BLO) in machine learning and vision, unifying various complex problems under a single framework and discussing algorithmic strategies and future directions.

Contribution

It offers a unified perspective on BLO, reformulates problems into a single-level framework, and analyzes gradient-based methods with convergence and complexity insights.

Findings

Unified BLO framework for learning and vision problems

Single-level reformulation simplifies complex hierarchical problems

Analysis of gradient-based BLO algorithms and their properties

Abstract

Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks, where one task is nested inside the other. In machine learning and computer vision fields, despite the different motivations and mechanisms, a lot of complex problems, such as hyper-parameter optimization, multi-task and meta-learning, neural architecture search, adversarial learning and deep reinforcement learning, actually all contain a series of closely related subproblms. In this paper, we first uniformly express these complex learning and vision problems from the perspective of BLO. Then we construct a best-response-based single-level reformulation and establish a unified algorithmic framework to understand and formulate mainstream gradient-based BLO methodologies, covering aspects ranging from fundamental automatic differentiation schemes to various accelerations, simplifications, extensions and their convergence and complexity properties. Last but not least, we discuss the potentials of our unified BLO framework for designing new algorithms and point out some promising directions for future research.