A Proximal Algorithm for Sampling from Non-smooth Potentials
This addresses a computational bottleneck in sampling for non-smooth potentials, offering incremental improvements in efficiency for machine learning and optimization applications.
The paper tackles sampling from non-smooth potentials by proposing a novel Markov chain Monte Carlo algorithm, achieving a polynomial-time complexity of ̃O(dε⁻¹) to reach ε total variation distance, which improves upon most existing results under similar assumptions.
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a polynomial-time complexity $\tilde {\cal O}(d\varepsilon^{-1})$ to obtain $\varepsilon$ total variation distance to the target density, better than most existing results under the same assumptions. Our method is based on the proximal bundle method and an alternating sampling framework. This framework requires the so-called restricted Gaussian oracle, which can be viewed as a sampling counterpart of the proximal mapping in convex optimization. One key contribution of this work is a fast algorithm that realizes the restricted Gaussian oracle for any convex non-smooth potential with bounded Lipschitz constant.