# Optimal Slice-Adaptive Tuning of Hybrid Slice Sampling

arXiv: https://arxiv.org/abs/2609.08172 · HTML: https://mlsanity.com/paper/2609.08172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Practical Coreset Constructions for Machine Learning](https://mlsanity.com/paper/1703.06476/) (2017)
- [Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions](https://mlsanity.com/paper/2110.00610/) (2021)
- [Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covariance](https://mlsanity.com/paper/1507.05780/) (2015)
- [Adaptive step size selection for Hessian-based manifold Langevin samplers](https://mlsanity.com/paper/1501.07454/) (2015)
- [Geodesic slice sampling on the sphere](https://mlsanity.com/paper/2301.08056/) (2023)
- [AutoStep: Locally adaptive involutive MCMC](https://mlsanity.com/paper/2410.18929/) (2024)
- [Markov Kernels Local Aggregation for Noise Vanishing Distribution Sampling](https://mlsanity.com/paper/1806.09000/) (2018)
- [Gibbsian polar slice sampling](https://mlsanity.com/paper/2302.03945/) (2023)
- [Parallel Affine Transformation Tuning of Markov Chain Monte Carlo](https://mlsanity.com/paper/2401.16567/) (2024)

## Abstract (arXiv)

Slice sampling is a Markov chain Monte Carlo algorithm that draws its next state uniformly from a "slice"---a super-level set of the target density function---at each iteration, thereby providing automatic local adaptivity to the scale of the target. In practice the exact slice is not known, so general-purpose implementations use an approximate slice that is grown from a starting interval of length w>0, with a computational cost that depends on w. This work presents an analysis of the average per-iteration number of target density evaluations, as a function of w, of hybrid slice sampling with various slice-finding schemes for targets with contiguous slices. The paper uses the results of the analysis to develop automated, slice-adaptive tuning schemes along with suboptimality bounds and asymptotic convergence guarantees. Simulations demonstrate that the tuning schemes reliably yield near-optimal slice-adaptive tuning with essentially no dependence on the initial setting of w.