Tensor Train for Global Optimization Problems in Robotics
This addresses the challenge of global optimization in robotics, offering a faster and more robust initialization method, though it appears incremental as it builds on tensor methods for existing solvers.
The authors tackled the problem of optimization convergence being sensitive to initial guesses by proposing a tensor-based method to initialize solvers near global optima, showing it can generate samples close to global optima and from multiple modes faster than existing methods in benchmarks and robotics applications like inverse kinematics and motion planning.
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.