The next IPAB Workshop will take place 21/01/2021 at 1pm via Blackboard Collaborate. The link can be found in the original email.
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.