Related papers: The Simulated Greedy Algorithm for Several Submodu…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
We introduce the notion of an online matroid embedding, which is an algorithm for mapping an unknown matroid that is revealed in an online fashion to a larger-but-known matroid. We establish the existence of such an embedding for binary…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy…
We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…
We study online secretary problems with returns in combinatorial packing domains with $n$ candidates that arrive sequentially over time in random order. The goal is to accept a feasible packing of candidates of maximum total value. In the…
In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given $n$ bidders each equipped with a general (not necessarily monotone) submodular utility and $m$ items that arrive online. The goal is to…
Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is…
Finding diverse solutions to optimization problems has been of practical interest for several decades, and recently enjoyed increasing attention in research. While submodular optimization has been rigorously studied in many fields, its…
Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks. For such problems, a simple greedy algorithm (\textsc{Greedy}) is guaranteed to find a solution achieving the objective with a…
This paper addresses the task allocation problem for multi-robot systems. The main issue with the task allocation problem is inherent complexity that makes finding an optimal solution within a reasonable time almost impossible. To hand the…
In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of $2$ for every order of the items. We show that if the valuations are…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured…
We consider a class of distributed submodular maximization problems in which each agent must choose a single strategy from its strategy set. The global objective is to maximize a submodular function of the strategies chosen by each agent.…
We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly…
During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. Partially linked to its numerous applications in mechanism design, substantial interest arose also in the…
Suppose a set of requests arrives online: each request gives some value $v_i$ if accepted, but requires using some amount of each of $d$ resources. Our cost is a convex function of the vector of total utilization of these $d$ resources.…