Stats, Optimization, and Machine Learning Seminar - Carl Mueller and Osman Malik
Carl Mueller, Department of Computer Science, University of Colorado Boulder
CHOMP: Gradient Optimization Techniques for Efficient Motion Planning
Existing high-dimensional motion planning algorithms are simultaneously overpowered and underpowered. Indomains sparsely populated by obstacles, the heuristics used by sampling-based planners to navigate “narrow passages” can be needlessly complex; furthermore, additional post-processing is required to remove the jerky or extraneous motions from the paths that such planners generate. In this paper, we present CHOMP, a novel method for continuous path refinement that uses covariant gradient techniques to improve the quality of sampled trajectories. Our optimization technique converges over a wider range of input paths and is able to optimize higherorder dynamics of trajectories than previous path optimization strategies. As a result, CHOMP can be used as a standalone motion planner in many real-world planning queries. The edfectiveness of our proposed method is demonstrated in manipulation planning for a 6-DOF robotic arm as well as in trajectory generation for a walking quadruped robot.
Osman Malik, Department of Applied Mathematics, University of Colorado Boulder
Low-rank Tucker decomposition of large tensors using TensorSketch
Many real datasets have more than two dimensions and are therefore better represented using tensors, or multi-way arrays, rather than matrices. In the same way that methods such as the singular value decomposition can help in the analysis of data in matrix form, tensor decompositions are important tools when working with tensor data. As multidimensional datasets grow larger and larger, there is an increasing need for methods that can handle them, even on modest hardware.
I will present results from recent research where we develop randomized algorithms for computing the Tucker decomposition of a tensor. Our algorithms, which utilize sketching and only need a single pass of the data, are suitable for decomposing large tensors when the decomposition we seek is of low-rank.
Tuesday, September 11, 2018 at 3:30pm
Engineering Center, ECCR 257
1111 Engineering Drive, Boulder, CO 80309