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

The Adaptive Seeding problem is an algorithmic challenge motivated by influence maximization in social networks: One seeks to select among certain accessible nodes in a network, and then select, adaptively, among neighbors of those nodes as they become accessible in order to maximize a global objective function. More generally, adaptive seeding is a stochastic optimization framework where the c...

Motivated by extremely large-scale machine learning problems, we introduce a new multistage algorithmic framework for submodular maximization (called MultGreed), where at each stage we apply an approximate greedy procedure to maximize surrogate submodular functions. The surrogates serve as proxies for a target submodular function but require less memory and are easy to evaluate. We theoreticall...

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 consider the problem of optimization from samples of monotone submodular functions with bounded curvature. In numerous applications, the function optimized is not known a priori, but instead learned from data. What are the guarantees we have when optimizing functions from sampled data? In this paper we show that for any monotone submodular function with curvature c there is a (1 c)/(1 + c c2...

Motivated by extremely large-scale machine learning problems, we introduce a new multistage algorithmic framework for submodular maximization (called MultGreed), where at each stage we apply an approximate greedy procedure to maximize surrogate submodular functions. The surrogates serve as proxies for a target submodular function but require less memory and are easy to evaluate. We theoreticall...

Sequence optimization, where the items in a list are ordered to maximize some reward has many applications such as web advertisement placement, search, and control libraries in robotics. Previous work in sequence optimization produces a static ordering that does not take any features of the item or context of the problem into account. In this work, we propose a general approach to order the ite...

In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network inference. Despite the apparent lack of convexity in such functions, we prove that stochastic projected gradient methods can provide strong approximation gu...

Submodular functions are a key concept in combinatorial optimization. Algorithms that involve submodular functions usually assume that they are given by a (value) oracle. Many interesting problems involving submodular functions can be solved using only polynomially many queries to the oracle, e.g., exact minimization or approximate maximization. In this paper, we consider the problem of approxi...