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Bi-Level Optimization (BLO) is originated from the area of economic gametheory and then introduced into the optimization community. BLO is able tohandle problems with a hierarchical structure, involving two levels ofoptimization tasks, where one task is nested inside the other. In machinelearning and computer vision fields, despite the different motivations andmechanisms, a lot of complex problems, such as hyper-parameter optimization,multi-task and meta-learning, neural architecture search, adversarial learningand deep reinforcement learning, actually all contain a series of closelyrelated subproblms. In this paper, we first uniformly express these complexlearning and vision problems from the perspective of BLO. Then we construct abest-response-based single-level reformulation and establish a unifiedalgorithmic framework to understand and formulate mainstream gradient-based BLOmethodologies, covering aspects ranging from fundamental automaticdifferentiation schemes to various accelerations, simplifications, extensionsand their convergence and complexity properties. Last but not least, we discussthe potentials of our unified BLO framework for designing new algorithms andpoint out some promising directions for future research.

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