CoCo: Online Mixed-Integer Control via Supervised Learning

Abhishek Cauligi, Preston Culbertson, Edward Schmerling, Mac Schwager, Bartolomeo Stellato, Marco Pavone

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
JournalIEEE Robotics and Automation Letters
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


  • Convex functions
  • data-driven optimization
  • mixed-integer convex programming
  • Optimization and optimal control
  • Planning
  • Robots
  • Supervised learning
  • Task analysis
  • Trajectory optimization
  • Upper bound


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