Submodular optimization, particularly under cardinality or cost constraints, has received considerable attention, stemming from its breadth of application, ranging from sensor placement to targeted marketing. However, the constraints faced in many real domains are more complex. We investigate an important and very general class of problems of maximizing a submodular function subject to general ...

Recent years have seen many algorithmic advances in the area of submodular optimization: (SO) min /max f(S) : S ∈ F , where F is a given family of feasible sets over a ground set V and f : 2 → R is submodular. This progress has been coupled with a wealth of new applications for these models. Our focus is on a more general class of multi-agent submodular optimization (MASO) which was introduced ...

In this paper we study the adaptive complexity of submodular optimization. Informally, the adaptive complexity of a problem is the minimal number of sequential rounds required to achieve a constant factor approximation when polynomially-many queries can be executed in parallel at each round. Adaptivity is a fundamental concept that is heavily studied in computer science, largely due to the need...

Many problems in Machine Learning can be modeled as submodular optimization problems. Recent work has focused on stochastic or adaptive versions of these problems. We consider the Scenario Submodular Cover problem, which is a counterpart to the Stochastic Submodular Cover problem studied by Golovin and Krause (2011). In Scenario Submodular Cover, the goal is to produce a cover with minimum expe...

We consider the submodular function minimization (SFM) and the quadratic minimization problems regularized by the Lovász extension of the submodular function. These optimization problems are intimately related; for example, min-cut problems and total variation denoising problems, where the cut function is submodular and its Lovász extension is given by the associated total variation. When a qua...

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize...

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast und...

We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial nature, submodular functions can be maximized approximately with strong theoretical guarantees in polynomial time. Typically, learning the submodular function a...

Citizens’ assemblies are groups of randomly selected constituents who tasked with providing recommendations on policy questions. Assembly members form their through a sequence discussions in small (deliberation), which group exchange arguments and experiences. We seek to support this process optimization, by studying how assign participants discussion over multiple sessions, way that maximizes ...