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In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
We consider a class of multi-agent optimal coverage problems in which the goal is to determine the optimal placement of a group of agents in a given mission space so that they maximize a coverage objective that represents a blend of…
We consider the sparse contextual bandit problem where arm feature affects reward through the inner product of sparse parameters. Recent studies have developed sparsity-agnostic algorithms based on the greedy arm selection policy. However,…
The compact genetic algorithm is an Estimation of Distribution Algorithm for binary optimisation problems. Unlike the standard Genetic Algorithm, no cross-over or mutation is involved. Instead, the compact Genetic Algorithm uses a virtual…
Achieving chemical accuracy in quantum simulations is often constrained by the measurement bottleneck: estimating operators requires a large number of shots, which remains costly even on fault-tolerant devices and is further exacerbated on…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
This paper proposes a greedy algorithm named as Big step greedy set cover algorithm to compute approximate minimum set cover. The Big step greedy algorithm, in each step selects p sets such that the union of selected p sets contains…
Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users in order to gain information that will lead to…
We consider parallel, or low adaptivity, algorithms for submodular function maximization. This line of work was recently initiated by Balkanski and Singer and has already led to several interesting results on the cardinality constraint and…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of…
We address the problem of efficient and unobstructed surveillance or communication in complex environments. On one hand, one wishes to use a minimal number of sensors to cover the environment. On the other hand, it is often important to…
Influence maximization is a prototypical problem enabling applications in various domains, and it has been extensively studied in the past decade. The classic influence maximization problem explores the strategies for deploying seed users…
We analyze the orthogonal greedy algorithm when applied to dictionaries $\mathbb{D}$ whose convex hull has small entropy. We show that if the metric entropy of the convex hull of $\mathbb{D}$ decays at a rate of $O(n^{-\frac{1}{2}-\alpha})$…
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
The classical problem of maximizing a submodular function under a matroid constraint is considered. Defining a new measure for the increments made by the greedy algorithm at each step, called the discriminant, improved approximation ratio…
In the adaptive influence maximization problem, we are given a social network and a budget $k$, and we iteratively select $k$ nodes, called seeds, in order to maximize the expected number of nodes that are reached by an influence cascade…
The challenge of discovering new molecules with desired properties is crucial in domains like drug discovery and material design. Recent advances in deep learning-based generative methods have shown promise but face the issue of sample…
We study the problem of estimating a random process from the observations collected by a network of sensors that operate under resource constraints. When the dynamics of the process and sensor observations are described by a state-space…
This article develops a new theoretical basis for decomposing signals that are formed by the linear superposition of a finite number of modes. Each mode depends nonlinearly upon several parameters; we seek both these parameters and the…