Related papers: Optimal Approximation Algorithms for Multi-agent C…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying…
In this paper, we study a class of online optimization problems with long-term budget constraints where the objective functions are not necessarily concave (nor convex) but they instead satisfy the Diminishing Returns (DR) property.…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…
Mini-batch gradient descent based methods are the de facto algorithms for training neural network architectures today. We introduce a mini-batch selection strategy based on submodular function maximization. Our novel submodular formulation…
We briefly discuss the greedy method and a couple of its more efficient variants for approximately maximizing monotone submodular functions.
Many sequential decision making problems can be formulated as an adaptive submodular maximization problem. However, most of existing studies in this field focus on pool-based setting, where one can pick items in any order, and there have…
Submodular maximization has been the backbone of many important machine-learning problems, and has applications to viral marketing, diversification, sensor placement, and more. However, the study of maximizing submodular functions has…
The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems…
In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the…
We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…
In many data-mining applications, including recommender systems, influence maximization, and team formation, the goal is to pick a subset of elements (e.g., items, nodes in a network, experts to perform a task) to maximize a monotone…
Combinatorial Auctions are a central problem in Algorithmic Mechanism Design: pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare, revenue, or profit). The…
We consider the maximization problem in the value oracle model of functions defined on $k$-tuples of sets that are submodular in every orthant and $r$-wise monotone, where $k\geq 2$ and $1\leq r\leq k$. We give an analysis of a…
Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…