The goal of a sequential decision-making problem is to design an interactive policy that adaptively selects group items, each selection based on the feedback from past, maximize expected utility selected items. It has been shown functions many real-world applications are adaptive submodular. However, most existing studies submodular optimization focus average-case, is, their objective find maxi...

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (suband super-differentials). The resulting algorithms, which repeatedly compute and then efficiently optimize submodular semigradients, offer new and generalize many old methods for submodular optimization. Our approach, moreover, takes s...

We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give diff...

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular functions, especially for minimization problems. While general submodular minimization is challenging, we propose a new method that exploits existing decomposab...

The conditional value at risk (CVaR) is a popular risk measure which enables risk-averse decision making under uncertainty. We consider maximizing the CVaR of a continuous submodular function, an extension of submodular set functions to a continuous domain. One example application is allocating a continuous amount of energy to each sensor in a network, with the goal of detecting intrusion or co...

In this paper we extend the classic problem of finding the maximum weight Hamiltonian cycle in a graph to the case where the objective is a submodular function of the edges. We consider a greedy algorithm and a 2-matching based algorithm, and we show that they have approximation factors of 1 2+κ and max{ 2 3(2+κ) , 2 3(1− κ)} respectively, where κ is the curvature of the submodular function. Bo...

We define an extension of matroid rank submodularity called R-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to R-submodularity. We apply R-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the Z-Rayleigh matroids. First, we show that the class of exten...

A number of combinatorial optimization problems in machine learning can be described as the problem of minimizing a submodular function. It is known that the unconstrained submodular minimization problem can be solved in strongly polynomial time. However, additional constraints make the problem intractable in many settings. In this paper, we discuss the submodular minimization under a size cons...

The theory of principal partitions of discrete systems such as graphs, matrices, matroids, and submodular systems has been developed since 1968. In the early stage of the developments during 1968–75 the principal partition was considered as a decomposition of a discrete system into its components together with a partially ordered structure of the set of the components. It then turned out that s...