ARTICLE Shetty_IJRR_2024/IDIAP Tensor Train for Global Optimization Problems in Robotics Shetty, Suhan Lembono, Teguh Santoso Löw, Tobias Calinon, Sylvain Global optimization multilinear algebra multimodal optimization tensor factorization tensor train decomposition tensor-variate cross approximation EXTERNAL http://publications.idiap.ch/attachments/papers/2024/Shetty_IJRR_2024.pdf PUBLIC International Journal of Robotics Research 43 6 811-839 0278-3649 1741-3176 2024 https://doi.org/10.1177/02783649231217527 doi The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization solvers near global optima. Our method does not require access to a database of good solutions. We first transform the cost function, which depends on both task parameters and optimization variables, into a probability density function. Unlike existing approaches, the joint probability distribution of the task parameters and optimization variables is approximated using the Tensor Train model, which enables efficient conditioning and sampling. We treat the task parameters as random variables, and for a given task, we generate samples for decision variables from the conditional distribution to initialize the optimization solver. Our method can produce multiple solutions (when they exist) faster than existing methods. We first evaluate the approach on benchmark functions for numerical optimization that are hard to solve using gradient-based optimization solvers with a naive initialization. The results show that the proposed method can generate samples close to global optima and from multiple modes. We then demonstrate the generality and relevance of our framework to robotics by applying it to inverse kinematics with obstacles and motion planning problems with a 7-DoF manipulator.