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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…
The problem of selecting a small-size representative summary of a large dataset is a cornerstone of machine learning, optimization and data science. Motivated by applications to recommendation systems and other scenarios with query-limited…
Sparse approximation is important in many applications because of concise form of an approximant and good accuracy guarantees. The theory of compressed sensing, which proved to be very useful in the image processing and data sciences, is…
Submodular function maximization finds application in a variety of real-world decision-making problems. However, most existing methods, based on greedy maximization, assume it is computationally feasible to evaluate F, the function being…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
We investigate the performance of m-th order consensus systems with stochastic external perturbations, where a subset of leader nodes incorporates absolute information into their control laws. The system performance is measured by its…
In the context of Gaussian conditioning, greedy algorithms iteratively select the most informative measurements, given an observed Gaussian random variable. However, the convergence analysis for conditioning Gaussian random variables…
In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent direction} has a favorable local behavior. In view of its global…
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…
This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…
We consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit,…
In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the…
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…
This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value…
We show for several computational problems how classical greedy algorithms for special cases can be derived in a simple way from dynamic programs for the general case: interval scheduling (restricted to unit weights), knapsack (restricted…
Recent work by Mania et al. has proved that certainty equivalent control achieves nearly optimal regret for linear systems with quadratic costs. However, when parameter uncertainty is large, certainty equivalence cannot be relied upon to…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…