IPAB Workshop-21/01/2021

Title: Persistent Homology for Warm-starting Optimal Control Abstract: Shooting methods are an efficient approach to solving non-linear optimal control problems. In practice, the solutions contain discontinuities introduced by system dynamics or the environment. Additionally, in many cases multiple equally suitable solutions exist to solve a problem. This makes optimal control difficult to warm-start using such trajectories. Towards this, recent work has focused on providing an initial guess from a learned model trained on samples generated during an offline exploration of the problem space. However, classic learning approaches smooth across the boundary of these discontinuities and thus generalize poorly. I will present a method based on persistent homology to automatically cluster the dataset of precomputed solutions to obtain different candidate initial guesses. We then train a Mixture-of-Experts within each cluster to predict initial guesses and provide a comparison with modality-agnostic learning. We use the tools from algebraic topology to extract information on the underlying structure of the solution space and I will discuss the different ways these tools can be used on trajectory data from dynamical systems.