Matches in SemOpenAlex for { <https://semopenalex.org/work/W3170252003> ?p ?o ?g. }
- W3170252003 abstract "It has been well established that first order optimization methods canconverge to the maximal objective value of concave functions and provideconstant factor approximation guarantees for (non-convex/non-concave)continuous submodular functions. In this work, we initiate the study of themaximization of functions of the form $F(x) = G(x) +C(x)$ over a solvableconvex body $P$, where $G$ is a smooth DR-submodular function and $C$ is asmooth concave function. This class of functions is a strict extension of bothconcave and continuous DR-submodular functions for which no theoreticalguarantee is known. We provide a suite of Frank-Wolfe style algorithms, which,depending on the nature of the objective function (i.e., if $G$ and $C$ aremonotone or not, and non-negative or not) and on the nature of the set $P$(i.e., whether it is downward closed or not), provide $1-1/e$, $1/e$, or $1/2$approximation guarantees. We then use our algorithms to get a framework tosmoothly interpolate between choosing a diverse set of elements from a givenground set (corresponding to the mode of a determinantal point process) andchoosing a clustered set of elements (corresponding to the maxima of a suitableconcave function). Additionally, we apply our algorithms to various functionsin the above class (DR-submodular + concave) in both constrained andunconstrained settings, and show that our algorithms consistently outperformnatural baselines." @default.
- W3170252003 created "2021-06-22" @default.
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- W3170252003 date "2021-06-09" @default.
- W3170252003 modified "2023-09-27" @default.
- W3170252003 title "Submodular + Concave." @default.
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