  Operator splitting methods have been successfully used in computational
sciences, statistics, learning and vision areas to reduce complex problems into
a series of simpler subproblems. However, prevalent splitting schemes are
mostly established only based on the mathematical properties of some general
optimization models. So it is a laborious process and often requires many
iterations of ideation and validation to obtain practical and task-specific
optimal solutions, especially for nonconvex problems in real-world scenarios.
To break through the above limits, we introduce a new algorithmic framework,
called Learnable Bregman Splitting (LBS), to perform deep-architecture-based
operator splitting for nonconvex optimization based on specific task model.
Thanks to the data-dependent (i.e., learnable) nature, our LBS can not only
speed up the convergence, but also avoid unwanted trivial solutions for
real-world tasks. Though with inexact deep iterations, we can still establish
the global convergence and estimate the asymptotic convergence rate of LBS only
by enforcing some fairly loose assumptions. Extensive experiments on different
applications (e.g., image completion and deblurring) verify our theoretical
results and show the superiority of LBS against existing methods.
