Related papers: Approximation Guarantees of Local Search Algorithm…

Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs…

We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it. We show that…

In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in…

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…

Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made…

This paper introduces a local optimization-based approach to test statistical hypotheses and to construct confidence intervals. This approach can be viewed as an extension of bootstrap, and yields asymptotically valid tests and confidence…

This paper proposes a binarization scheme for vectors of high dimension based on the recent concept of anti-sparse coding, and shows its excellent performance for approximate nearest neighbor search. Unlike other binarization schemes, this…

This work focuses on the convergence analysis of adaptive distributed beamforming schemes that can be reformulated as local random search algorithms via a random search framework. Once reformulated as local random search algorithms, it is…

Data coding as a building block of several image processing algorithms has been received great attention recently. Indeed, the importance of the locality assumption in coding approaches is studied in numerous works and several methods are…

In this paper, we develop upon the topic of loss function learning, an emergent meta-learning paradigm that aims to learn loss functions that significantly improve the performance of the models trained under them. Specifically, we propose a…

In this paper we consider the classical maximum set packing problem where set cardinality is upper bounded by $k$. We show how to design a variant of a polynomial-time local search algorithm with performance guarantee $(k+2)/3$. This local…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

Sparse structure learning in high-dimensional Gaussian graphical models is an important problem in multivariate statistical signal processing; since the sparsity pattern naturally encodes the conditional independence relationship among…

An overview of some methods of statistical physics applied to the analysis of algorithms for optimization problems (satisfiability of Boolean constraints, vertex cover of graphs, decoding, ...) with distributions of random inputs is…

There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of…

Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

This paper is motivated by structured sparsity for deep neural network training. We study a weighted group L0-norm constraint, and present the projection and normal cone of this set. Using randomized smoothing, we develop zeroth and…

Inspired by the fact that human brains can emphasize discriminative parts of the input and suppress irrelevant ones, substantial local mechanisms have been designed to boost the development of computer vision. They can not only focus on…

Researchers are exploring novel computational paradigms such as sparse coding and neuromorphic computing to bridge the efficiency gap between the human brain and conventional computers in complex tasks. A key area of focus is neuromorphic…

Local search is a powerful heuristic in optimization and computer science, the complexity of which has been studied in the white box and black box models. In the black box model, we are given a graph $G = (V,E)$ and oracle access to a…