Proximal Oracles for Optimization and Sampling

arXiv:2404.02239v1 Announce Type: cross
Abstract: We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is either semi-smooth or in composite form as the finite sum of semi-smooth components. To overcome the challenges caused by non-smoothness, our algorithms employ two powerful proximal frameworks in optimization and sampling: the proximal point framework for optimization and the alternating sampling framework (ASF) that uses …

abstract arxiv challenges components cs.lg form function math.oc negative optimization sampling study type