  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.
