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Shooting methods are an efficient approach to solving nonlinear optimalcontrol problems. As they use local optimization, they exhibit favorableconvergence when initialized with a good warm-start but may not converge at allif provided with a poor initial guess. Recent work has focused on providing aninitial guess from a learned model trained on samples generated during anoffline exploration of the problem space. However, in practice the solutionscontain discontinuities introduced by system dynamics or the environment.Additionally, in many cases multiple equally suitable, i.e., multi-modal,solutions exist to solve a problem. Classic learning approaches smooth acrossthe boundary of these discontinuities and thus generalize poorly. In this work,we apply tools from algebraic topology to extract information on the underlyingstructure of the solution space. In particular, we introduce a method based onpersistent homology to automatically cluster the dataset of precomputedsolutions to obtain different candidate initial guesses. We then train aMixture-of-Experts within each cluster to predict state and controltrajectories to warm-start the optimal control solver and provide a comparisonwith modality-agnostic learning. We demonstrate our method on a cart-pole toyproblem and a quadrotor avoiding obstacles, and show that clustering samplesbased on inherent structure improves the warm-start quality.

Memory Clustering using Persistent Homology for Multimodality- and Discontinuity-Sensitive Learning of Optimal Control Warm-starts