In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies
<|reference_start|>In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies: We present a new random walk for uniformly sampling high-dimensional convex bodies. It achieves state-of-the-art runtime complexity with stronger guarantees on the output than previously known, namely in R\'enyi divergence (which implies TV, $\mathcal{W}_2$, KL, $\chi^2$). The proof departs from known approaches for polytime algorithms for the problem -- we utilize a stochastic diffusion perspective to show contraction to the target distribution with the rate of convergence determined by functional isoperimetric constants of the stationary density.<|reference_end|>
@article{kook2024in-and-out:,
    title={In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies},
    author={Yunbum Kook, Santosh S. Vempala, Matthew S. Zhang},
    journal={arXiv preprint arXiv:2405.01425},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.01425},
    primaryClass={cs.DS cs.LG math.ST stat.ML stat.TH}
}