# Incorporating Local Step-Size Adaptivity into the No-U-Turn Sampler using Gibbs Self Tuning

arXiv: https://arxiv.org/abs/2408.08259 · HTML: https://mlsanity.com/paper/2408.08259/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2024.

## Built on by (most cited first, 7 of 7)

- [AutoStep: Locally adaptive involutive MCMC](https://mlsanity.com/paper/2410.18929/) (2024)
- [A Langevin sampling algorithm inspired by the Adam optimizer](https://mlsanity.com/paper/2504.18911/) (2025)
- [The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler](https://mlsanity.com/paper/2506.18746/) (2025)
- [On Accelerated Mixing of the No-U-turn Sampler](https://mlsanity.com/paper/2507.13259/) (2025)
- [Asymptotically exact variational flows via involutive MCMC kernels](https://mlsanity.com/paper/2506.02162/) (2025)
- [A Theoretical Comparison of No-U-Turn Sampler Variants: Necessary and Sufficient Convergence Conditions and Mixing Time Analysis under Gaussian Targets](https://mlsanity.com/paper/2603.18640/) (2026)
- [ATLAS: Adapting Trajectory Lengths and Step-Size for Hamiltonian Monte Carlo](https://mlsanity.com/paper/2410.21587/) (2024)

## Abstract (arXiv)

Adapting the step size locally in the no-U-turn sampler (NUTS) is challenging because the step-size and path-length tuning parameters are interdependent. The determination of an optimal path length requires a predefined step size, while the ideal step size must account for errors along the selected path. Ensuring reversibility further complicates this tuning problem. In this paper, we present a method for locally adapting the step size in NUTS that is an instance of the Gibbs self-tuning (GIST) framework. Our approach guarantees reversibility with an acceptance probability that depends exclusively on the conditional distribution of the step size. We validate our step-size-adaptive NUTS method on Neal's funnel density and a high-dimensional normal distribution, demonstrating its effectiveness in challenging scenarios.