# Hit-and-Run for Sampling and Planning in Non-Convex Spaces

arXiv: https://arxiv.org/abs/1610.08865 · HTML: https://mlsanity.com/paper/1610.08865/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2016.

## Built on by (most cited first, 3 of 3)

- [Quantum Speedups of Optimizing Approximately Convex Functions with Applications to Logarithmic Regret Stochastic Convex Bandits](https://mlsanity.com/paper/2209.12897/) (2022)
- [On the choice of the non-trainable internal weights in random feature maps](https://mlsanity.com/paper/2408.03626/) (2024)
- [The Geometry of Efficient Nonconvex Sampling](https://mlsanity.com/paper/2603.25622/) (2026)

## Abstract (arXiv)

We propose the Hit-and-Run algorithm for planning and sampling problems in non-convex spaces. For sampling, we show the first analysis of the Hit-and-Run algorithm in non-convex spaces and show that it mixes fast as long as certain smoothness conditions are satisfied. In particular, our analysis reveals an intriguing connection between fast mixing and the existence of smooth measure-preserving mappings from a convex space to the non-convex space. For planning, we show advantages of Hit-and-Run compared to state-of-the-art planning methods such as Rapidly-Exploring Random Trees.