  Many robotics problems, from robot motion planning to object manipulation,
can be modeled as mixed-integer convex programs (MICPs). However,
state-of-the-art algorithms are still unable to solve MICPs for control
problems quickly enough for online use and existing heuristics can typically
only find suboptimal solutions that might degrade robot performance. In this
work, we turn to data-driven methods and present the Combinatorial Offline,
Convex Online (CoCo) algorithm for quickly finding high quality solutions for
MICPs. CoCo consists of a two-stage approach. In the offline phase, we train a
neural network classifier that maps the problem parameters to a (logical
strategy), which we define as the discrete arguments and relaxed big-M
constraints associated with the optimal solution for that problem. Online, the
classifier is applied to select a candidate logical strategy given new problem
parameters; applying this logical strategy allows us to solve the original MICP
as a convex optimization problem. We show through numerical experiments how
CoCo finds near optimal solutions to MICPs arising in robot planning and
control with 1 to 2 orders of magnitude solution speedup compared to other
data-driven approaches and solvers.
