Related papers: Submodular Optimization Problems and Greedy Strate…
We consider the celebrated bound introduced by Conforti and Cornu\'ejols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy…
Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
Multimodal learning considers learning from multi-modality data, aiming to fuse heterogeneous sources of information. However, it is not always feasible to leverage all available modalities due to memory constraints. Further, training on…
In this paper, we propose a unified framework and an algorithm for the problem of group recommendation where a fixed number of items or alternatives can be recommended to a group of users. The problem of group recommendation arises…
We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the…
Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…
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 the leader selection problem in a network with consensus dynamics where both leader and follower agents are subject to stochastic external disturbances. The performance of the system is quantified by the total steady-state…
We consider an optimization problem where the decision variable is a string of bounded length. For some time there has been an interest in bounding the performance of the greedy strategy for this problem. Here, we provide weakened…
We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for…
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 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…
We consider the problem of studying the performance of greedy algorithm on sensor selection problem for stable linear systems with Kalman Filter. Specifically, the objective is to find the system parameters that affects the performance of…
The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
We consider stochastic influence maximization problems arising in social networks. In contrast to existing studies that involve greedy approximation algorithms with a 63% performance guarantee, our work focuses on solving the problem…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
The Greedy algorithm is the simplest heuristic in sequential decision problem that carelessly takes the locally optimal choice at each round, disregarding any advantages of exploring and/or information gathering. Theoretically, it is known…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
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…
Many algorithms for maximizing a monotone submodular function subject to a knapsack constraint rely on the natural greedy heuristic. We present a novel refined analysis of this greedy heuristic which enables us to: $(1)$ reduce the…