From Linear to Linearizable Optimization: A Novel Framework with Applications to Stationary and Non-stationary DR-submodular Optimization

arXiv:2405.00065v1 Announce Type: cross
Abstract: This paper introduces the notion of upper linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in various settings, including monotone and non-monotone cases over different convex sets. A general meta-algorithm is devised to convert algorithms for linear/quadratic maximization into ones that optimize upper quadratizable functions, offering a unified approach to tackling concave and DR-submodular optimization problems. The paper extends these results to multiple feedback settings, facilitating conversions between semi-bandit/first-order feedback and bandit/zeroth-order feedback, as …

abstract algorithm algorithms applications arxiv cases class cs.cc cs.lg framework functions general linear math.oc meta notion novel optimization paper stat.ml type