In this paper, we study the problem of constrained and stochastic continuous submodular maximization. Even though the objective function is not concave (nor convex) and is defined in terms of an expectation, we develop a variant of the conditional gradient method, called Stochastic Continuous Greedy, which achieves a tight approximation guarantee. More precisely, for a monotone and continuous D...

We introduce submodular optimization to the problem of training data subset selection for statistical machine translation (SMT). By explicitly formulating data selection as a submodular program, we obtain fast scalable selection algorithms with mathematical performance guarantees, resulting in a unified framework that clarifies existing approaches and also makes both new and many previous appro...

We study simultaneous learning and covering problems: submodular set cover problems that depend on the solution to an active (query) learning problem. The goal is to jointly minimize the cost of both learning and covering. We extend recent work in this setting to allow for a limited amount of adversarial noise. Certain noisy query learning problems are a special case of our problem. Crucial to ...

We prove canonical and non-canonical tree-of-tangles theorems for abstract separation systems that are merely structurally submodular. Our results imply all known graphs, matroids with submodular order functions, greatly simplified shortened proofs.

We introduce a class of discrete point processes that we call the Submodular Point Processes (SPPs). These processes are characterized via a submodular (or supermodular) function, and naturally model notions of information, coverage and diversity, as well as cooperation. Unlike Log-submodular and Log-supermodular distributions (Log-SPPs) such as determinantal point processes (DPPs), SPPs are th...

We study settings in which autonomous agents are designed to optimize a given system-level objective. In typical approaches this problem, each agent is endowed with decision-making rule that specifies the agent’s choice as function of relevant information pertaining system’s state. The choices other system comprise key component information. This paper considers scenario rules not implementable...