We study the canonical problem of maximizing a stochastic submodular function subject to cardinality constraint, where goal is select subset from ground set items with uncertain individual performances maximize their expected group value. Although near-optimal algorithms have been proposed for this problem, practical concerns regarding scalability, compatibility distributed implementation, and ...

The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem are rarely known exactly, and using wrong parameters can lead to undesirable outcomes. We hence revisit a continuous version of the Budget Allocation or Bipar...

In this lecture, the focus is on submodular function in combinatorial optimizations. The first class of submodular functions which was studied thoroughly was the class of matroid rank functions. The flourishing stage of matroid theory came with Jack Edmonds’ work in 1960s, when he gave a minmax formula and an efficient algorithm to the matroid partition problem, from which the matroid intersect...

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, submodular functions or supermodular functions separately while maintaining polynomial time computation. In this work, a novel generic convex ...

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a simple single objective evolutionary algorithm called (1 + 1) EA and a multiobjective evolutionary algorithm called GSEMO until they have obtai...

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization problems are often too large to be solved on a single machine. We develop a simple distributed algorithm that is embarrassingly parallel and it achieves prova...

The submodular function minimization problem (SFM) is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial-time algorithms have recently been discovered to solve this problem. The most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally-ordered nite set and whose range includ...

Many prediction domains, such as ad placement, recommendation, trajectory prediction, and document summarization, require predicting a set or list of options. Such lists are often evaluated using submodular reward functions that measure both quality and diversity. We propose a simple, efficient, and provably near-optimal approach to optimizing such prediction problems based on noregret learning...