Related papers: Submodular Welfare Maximization
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 study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
Migration presents sweeping societal challenges that have recently attracted significant attention from the scientific community. One of the prominent approaches that have been suggested employs optimization and machine learning to match…
We study the Nash Social Welfare problem: Given $n$ agents with valuation functions $v_i:2^{[m]} \rightarrow {\mathbb R}$, partition $[m]$ into $S_1,\ldots,S_n$ so as to maximize $(\prod_{i=1}^{n} v_i(S_i))^{1/n}$. The problem has been…
We introduce the problem of maximizing approximately $k$-submodular functions subject to size constraints. In this problem, one seeks to select $k$-disjoint subsets of a ground set with bounded total size or individual sizes, and maximum…
We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial…
Designing an incentive-compatible auction mechanism that maximizes the auctioneer's revenue while minimizes the bidders' ex-post regret is an important yet intricate problem in economics. Remarkable progress has been achieved through…
Research on promoting cooperation among autonomous, self-regarding agents has often focused on the bi-objective optimisation problem: minimising the total incentive cost while maximising the frequency of cooperation. However, the optimal…
The goal of a sequential decision making problem is to design an interactive policy that adaptively selects a group of items, each selection is based on the feedback from the past, in order to maximize the expected utility of selected…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
Most of existing studies on submodular maximization focus on selecting a subset of items that maximizes a \emph{single} submodular function. However, in many real-world scenarios, we might have multiple user-specific functions, each of…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides $m^{\frac 1 2 -\epsilon}$ approximation to the social welfare and uses value queries only must use…
Computational and economic results suggest that social welfare maximization and combinatorial auction design are much easier when bidders' valuations satisfy the "gross substitutes" condition. The goal of this paper is to evaluate…
We study incentive compatible mechanisms for Combinatorial Auctions where the bidders have submodular (or XOS) valuations and are budget-constrained. Our objective is to maximize the \emph{liquid welfare}, a notion of efficiency for…
Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…