Keywords: optimal control, convex optimization, mixed-integer programming
TL;DR: Combining supervised learning and parametric optimization approaches to efficiently solve mixed-integer convex optimization programs for robot control.
Abstract: Mixed-integer convex programming (MICP) is a popular modeling framework for solving discrete and combinatorial optimization problems arising in various settings. Despite advances in efficient solvers for numerical optimization problems, MICPs remain challenging to solve for real-time control in applications requiring solution rates of 10-100Hz. Seeking to bridge this gap, we present an approach that leverages results from supervised learning and parametric programming to quickly solve for feasible solutions to MICPs. This approach consists of (1) an offline phase where a classifier is trained on a codebook consisting of solved MICPs and (2) an online step where the network yields candidate strategies given a new set of problem parameters. Unlike other data-driven approaches for solving MICPs, we show that our approach can tackle a broad category of problems that can be modeled as MICPs and how our framework can handle problems with a different number of discrete decision variables than the problems in the training set. Finally, we demonstrate the efficacy of our proposed approach through numerical experiments showing improved solution times and optimality compared to existing approaches for solving MICPs.