# Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics

arXiv: https://arxiv.org/abs/1605.04636 · HTML: https://mlsanity.com/paper/1605.04636/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2016.

## Built on by (most cited first, 4 of 4)

- [Discontinuity-Sensitive Optimal Control Learning by Mixture of Experts](https://mlsanity.com/paper/1803.02493/) (2018)
- [Tensor Train for Global Optimization Problems in Robotics](https://mlsanity.com/paper/2206.05077/) (2022)
- [CoverLib: Classifiers-equipped Experience Library by Iterative Problem Distribution Coverage Maximization for Domain-tuned Motion Planning](https://mlsanity.com/paper/2405.02968/) (2024)
- [Path Database Guidance for Motion Planning](https://mlsanity.com/paper/2504.05550/) (2025)

## Abstract (arXiv)

This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near-globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics (IK) problems, wherein large solution databases are used to produce near-optimal solutions in sub-millisecond time on a standard PC.