# Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimization

arXiv: https://arxiv.org/abs/2509.17405 · HTML: https://mlsanity.com/paper/2509.17405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 55 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 29 of 29)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [On Information Gain and Regret Bounds in Gaussian Process Bandits](https://mlsanity.com/paper/2009.06966/) (2020)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Statistical and Topological Properties of Sliced Probability Divergences](https://mlsanity.com/paper/2003.05783/) (2020)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [A survey on high-dimensional Gaussian process modeling with application to Bayesian optimization](https://mlsanity.com/paper/2111.05040/) (2021)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Optimization, fast and slow: optimally switching between local and Bayesian optimization](https://mlsanity.com/paper/1805.08610/) (2018)
- [Convergence Guarantees for Adaptive Bayesian Quadrature Methods](https://mlsanity.com/paper/1905.10271/) (2019)
- [Quasi-Monte Carlo for 3D Sliced Wasserstein](https://mlsanity.com/paper/2309.11713/) (2023)
- [Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees](https://mlsanity.com/paper/1506.02681/) (2015)
- [Bayesian Optimization with Exponential Convergence](https://mlsanity.com/paper/1604.01348/) (2016)
- [GPflowOpt: A Bayesian Optimization Library using TensorFlow](https://mlsanity.com/paper/1711.03845/) (2017)
- [High-Dimensional Bayesian Optimization via Nested Riemannian Manifolds](https://mlsanity.com/paper/2010.10904/) (2020)
- [Sliced Wasserstein Estimation with Control Variates](https://mlsanity.com/paper/2305.00402/) (2023)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [Sliced Wasserstein with Random-Path Projecting Directions](https://mlsanity.com/paper/2401.15889/) (2024)
- [Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection](https://mlsanity.com/paper/2109.09264/) (2021)
- [Markovian Sliced Wasserstein Distances: Beyond Independent Projections](https://mlsanity.com/paper/2301.03749/) (2023)
- [Constrained Bayesian Optimization for Automatic Underwater Vehicle Hull Design](https://mlsanity.com/paper/2302.14732/) (2023)
- [Sliced-Wasserstein Estimation with Spherical Harmonics as Control Variates](https://mlsanity.com/paper/2402.01493/) (2024)
- [A User's Guide to Sampling Strategies for Sliced Optimal Transport](https://mlsanity.com/paper/2502.02275/) (2025)
- [Sample-Efficient and Surrogate-Based Design Optimization of Underwater Vehicle Hulls](https://mlsanity.com/paper/2304.12420/) (2023)
- [LABCAT: Locally adaptive Bayesian optimization using principal-component-aligned trust regions](https://mlsanity.com/paper/2311.11328/) (2023)
- [Repulsive Monte Carlo on the sphere for the sliced Wasserstein distance](https://mlsanity.com/paper/2509.10166/) (2025)

## Abstract (arXiv)

The sliced Wasserstein distance (SW) reduces optimal transport on ℝd to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work shows that quasi-Monte Carlo constructions for computing SW (QSW) yield direction sets with excellent approximation error. This paper presents an alternate, novel approach: learning directions with Bayesian optimization (BO), particularly in settings where SW appears inside an optimization loop (e.g., gradient flows). We introduce a family of drop-in selectors for projection directions: BOSW, a one-shot BO scheme on the unit sphere; RBOSW, a periodic-refresh variant; ABOSW, an adaptive hybrid that seeds from competitive QSW sets and performs a few lightweight BO refinements; and ARBOSW, a restarted hybrid that periodically relearns directions during optimization. Our BO approaches can be composed with QSW and its variants (demonstrated by ABOSW/ARBOSW) and require no changes to downstream losses or gradients. We provide numerical experiments where our methods achieve state-of-the-art performance, and on the experimental suite of the original QSW paper, we find that ABOSW and ARBOSW can achieve convergence comparable to the best QSW variants with modest runtime overhead.