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  "path": "/abs/2605.12461v1",
  "publishedAt": "2026-05-13T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Linghai Liu",
    "Sinho Chewi"
  ],
  "textContent": "**Authors:** Linghai Liu, Sinho Chewi\n\nWe propose an algorithm to sample from composite log-concave distributions over $\\mathbb{R}^d$, i.e., densities of the form $π\\propto e^{-f-g}$, assuming access to gradient evaluations of $f$ and a restricted Gaussian oracle (RGO) for $g$. The latter requirement means that we can easily sample from the density $\\text{RGO}_{g,h,y}(x) \\propto \\exp(-g(x) -\\frac{1}{2h}||y-x||^2)$, which is the sampling analogue of the proximal operator for $g$. If $f + g$ is $α$-strongly convex and $f$ is $β$-smooth, our sampler achieves $\\varepsilon$ error in total variation distance in $\\widetilde{\\mathcal O}(κ\\sqrt d \\log^4(1/\\varepsilon))$ iterations where $κ:= β/α$, which matches prior state-of-the-art results for the case $g=0$. We further extend our results to cases where (1) $π$ is non-log-concave but satisfies a Poincaré or log-Sobolev inequality, and (2) $f$ is non-smooth but Lipschitz.",
  "title": "A proximal gradient algorithm for composite log-concave sampling"
}