A proximal gradient algorithm for composite log-concave sampling

arXiv:2605.12461v1 Announce Type: cross Abstract: We propose an algorithm to sample from composite log-concave distributions over R^d, i.e., densities of the form pipropto 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 ext{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 alpha-strongly convex and f is eta-smooth, our sampler achieves arepsilon error in total variation distance in widetilde{mathcal O}(kappa sqrt d log^4(1/arepsilon)) iterations where kappa := eta/alpha, which matches prior state-of-the-art results for the case g=0. We further extend our results to cases where (1) pi is non-log-concave but satisfies a Poincare or log-Sobolev inequality, and (2) f is non-smooth but Lipschitz.

Source: arXiv cs.LG | 2026-05-13