  Gradient methods have become mainstream techniques for Bi-Level Optimization
(BLO) in learning and vision fields. The validity of existing works heavily
relies on solving a series of approximation subproblems with extraordinarily
high accuracy. Unfortunately, to achieve the approximation accuracy requires
executing a large quantity of time-consuming iterations and computational
burden is naturally caused. This paper is thus devoted to address this critical
computational issue. In particular, we propose a single-level formulation to
uniformly understand existing explicit and implicit Gradient-based BLOs
(GBLOs). This together with our designed counter-example can clearly illustrate
the fundamental numerical and theoretical issues of GBLOs and their naive
accelerations. By introducing the dual multipliers as a new variable, we then
establish Bilevel Alternating Gradient with Dual Correction (BAGDC), a general
framework, which significantly accelerates different categories of existing
methods by taking specific settings. A striking feature of our convergence
result is that, compared to those original unaccelerated GBLO versions, the
fast BAGDC admits a unified non-asymptotic convergence theory towards
stationarity. A variety of numerical experiments have also been conducted to
demonstrate the superiority of the proposed algorithmic framework.
