# Tensor Train for Global Optimization Problems in Robotics

arXiv: https://arxiv.org/abs/2206.05077 · HTML: https://mlsanity.com/paper/2206.05077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 71 references that are in the map.
- First posted on arXiv 10 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)
- [Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control](https://mlsanity.com/paper/1909.04947/) (2019)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [TTOpt: A Maximum Volume Quantized Tensor Train-based Optimization and its Application to Reinforcement Learning](https://mlsanity.com/paper/2205.00293/) (2022)
- [Motion Planning by Learning the Solution Manifold in Trajectory Optimization](https://mlsanity.com/paper/2107.05842/) (2021)
- [Multimodal Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2003.07054/) (2020)
- [Probabilistic Modeling with Matrix Product States](https://mlsanity.com/paper/1902.06888/) (2019)
- [Memory of Motion for Warm-starting Trajectory Optimization](https://mlsanity.com/paper/1907.01474/) (2019)
- [Linear Hamilton Jacobi Bellman Equations in High Dimensions](https://mlsanity.com/paper/1404.1089/) (2014)
- [Ergodic Exploration using Tensor Train: Applications in Insertion Tasks](https://mlsanity.com/paper/2101.04428/) (2021)
- [Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics](https://mlsanity.com/paper/1605.04636/) (2016)
- [Learning How to Walk: Warm-starting Optimal Control Solver with Memory of Motion](https://mlsanity.com/paper/2001.11751/) (2020)
- [Learning from demonstration using products of experts: applications to manipulation and task prioritization](https://mlsanity.com/paper/2010.03505/) (2020)
- [Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series](https://mlsanity.com/paper/2104.10731/) (2021)
- [TTML: tensor trains for general supervised machine learning](https://mlsanity.com/paper/2203.04352/) (2022)

## Built on by (most cited first, 2 of 2)

- [Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluations](https://mlsanity.com/paper/2304.12875/) (2023)
- [Black-Box Approximation and Optimization with Hierarchical Tucker Decomposition](https://mlsanity.com/paper/2402.02890/) (2024)

## Abstract (arXiv)

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.