# Composite Logconcave Sampling with a Restricted Gaussian Oracle

arXiv: https://arxiv.org/abs/2006.05976 · HTML: https://mlsanity.com/paper/2006.05976/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [A Proximal Algorithm for Sampling from Non-smooth Potentials](https://mlsanity.com/paper/2110.04597/) (2021)
- [A Proximal Algorithm for Sampling](https://mlsanity.com/paper/2202.13975/) (2022)
- [Bregman Proximal Langevin Monte Carlo via Bregman--Moreau Envelopes](https://mlsanity.com/paper/2207.04387/) (2022)
- [Proximal Oracles for Optimization and Sampling](https://mlsanity.com/paper/2404.02239/) (2024)
- [Beyond Scores: Proximal Diffusion Models](https://mlsanity.com/paper/2507.08956/) (2025)
- [A Proximal Algorithm for Sampling from Non-convex Potentials](https://mlsanity.com/paper/2205.10188/) (2022)
- [Stochastic Langevin Differential Inclusions with Applications to Machine Learning](https://mlsanity.com/paper/2206.11533/) (2022)
- [Truncated Log-concave Sampling with Reflective Hamiltonian Monte Carlo](https://mlsanity.com/paper/2102.13068/) (2021)

## Abstract (arXiv)

We consider sampling from composite densities on ℝd of the form dπ(x) propto exp(-f(x) - g(x))dx for well-conditioned f and convex (but possibly non-smooth) g, a family generalizing restrictions to a convex set, through the abstraction of a restricted Gaussian oracle. For f with condition number kappa, our algorithm runs in O left(kappa2 d log2tfrackappa dεright) iterations, each querying a gradient of f and a restricted Gaussian oracle, to achieve total variation distance ε. The restricted Gaussian oracle, which draws samples from a distribution whose negative log-likelihood sums a quadratic and g, has been previously studied and is a natural extension of the proximal oracle used in composite optimization. Our algorithm is conceptually simple and obtains stronger provable guarantees and greater generality than existing methods for composite sampling. We conduct experiments showing our algorithm vastly improves upon the hit-and-run algorithm for sampling the restriction of a (non-diagonal) Gaussian to the positive orthant.