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We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…
Often times, in many design problems, there is a need to select a small set of informative or representative elements from a large ground set of entities in an optimal fashion. Submodular optimization that provides for a formal way to solve…
We demonstrate that from an algorithm guaranteeing an approximation factor for the ratio of submodular (RS) optimization problem, we can build another algorithm having a different kind of approximation guarantee -- weaker than the classical…
This paper addresses the optimal control problem known as the Linear Quadratic Regulator in the case when the dynamics are unknown. We propose a multi-stage procedure, called Coarse-ID control, that estimates a model from a few experimental…
Actuator placement is an active field of research which has received significant attention for its applications in complex dynamical networks. In this paper, we study the problem of finding a set of actuator placements minimizing the metric…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
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…
In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a…
The problem of optimally placing sensors under a cost constraint arises naturally in the design of industrial and commercial products, as well as in scientific experiments. We consider a relaxation of the full optimization formulation 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 number of scientific fields rely on placing permanent magnets in order to produce a desired magnetic field. We have shown in recent work that the placement process can be formulated as sparse regression. However, binary, grid-aligned…
We study the problem of maximizing a submodular function, subject to a cardinality constraint, with a set of agents communicating over a connected graph. We propose a distributed greedy algorithm that allows all the agents to converge to a…
Several sparsity-constrained algorithms such as Orthogonal Matching Pursuit or the Frank-Wolfe algorithm with sparsity constraints work by iteratively selecting a novel atom to add to the current non-zero set of variables. This selection…
In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade…
Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes…
We study the problem that requires a team of robots to perform joint localization and target tracking task while ensuring team connectivity and collision avoidance. The problem can be formalized as a nonlinear, non-convex optimization…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal. When this algorithm…
Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality…
In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…