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Most machine learning and deep neural network algorithms rely on certain iterative algorithms to optimise their utility/cost functions, e.g. Stochastic Gradient Descent. In distributed learning, the networked nodes have to work…
We consider the problem of maximizing non-negative non-decreasing set functions. Although most of the recent work focus on exploiting submodularity, it turns out that several objectives we encounter in practice are not submodular.…
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…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
This article provides a comprehensive exploration of submodular maximization problems, focusing on those subject to uniform and partition matroids. Crucial for a wide array of applications in fields ranging from computer science to systems…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
A $k$-submodular function is a generalization of the submodular set function. Many practical applications can be modeled as maximizing a $k$-submodular function, such as multi-cooperative games, sensor placement with $k$ type sensors,…
We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…
Collective communications are ubiquitous in parallel applications. We present two new algorithms for performing a reduction. The operation associated with our reduction needs to be associative and commutative. The two algorithms are…
Weak submodularity is a natural relaxation of the diminishing return property, which is equivalent to submodularity. Weak submodularity has been used to show that many (monotone) functions that arise in practice can be efficiently maximized…
Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing…
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…
Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity,…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
Simultaneous operation of all sensors in a large-scale sensor network is power-consuming and computationally expensive. Hence, it is desirable to select fewer sensors. A greedy algorithm is widely used for sensor selection in homogeneous…
This paper defines a generalized column subset selection problem which is concerned with the selection of a few columns from a source matrix A that best approximate the span of a target matrix B. The paper then proposes a fast greedy…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
In the classic sequential testing problem, we are given a system with several components each of which fails with some independent probability. The goal is to identify whether or not some component has failed. When the test costs are…
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 consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…