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.

翻译：双级最佳化(BLO)源自经济游戏理论领域,然后引入优化社区。BLO能够处理等级结构问题,涉及两个层次的优化任务,其中一项任务嵌入另一个层次。在机器学习和计算机视觉领域,尽管动机和机制不同,许多复杂问题,如超参数优化、多任务和元学习、神经结构搜索、对抗性学习和深强化学习,实际上都包含一系列密切相关的子项目。本文首先从BLO的角度统一表达这些复杂的学习和愿景问题。然后我们构建一个基于最佳反应的单一层次的重新拟订,并建立一个统一的算法框架,以理解和制定基于梯度的BLO方法的主流,涵盖从基本自动区分计划到各种加速、简化、扩展及其融合和复杂特性等各个方面。最后但并非最不重要的一点是,我们讨论了我们统一的BLO框架在设计新的算法和指出未来研究的有希望的方向方面的潜力。