  This paper describes a data-driven framework for approximate global
optimization in which precomputed solutions to a sample of problems are
retrieved and adapted during online use to solve novel problems. This approach
has promise for real-time applications in robotics, since it can produce
near-globally optimal solutions orders of magnitude faster than standard
methods. This paper establishes theoretical conditions on how many and where
samples are needed over the space of problems to achieve a given approximation
quality. The framework is applied to solve globally optimal collision-free
inverse kinematics (IK) problems, wherein large solution databases are used to
produce near-optimal solutions in sub-millisecond time on a standard PC.
