Related papers: Runtime Guarantees for Regression Problems

We propose a data-driven method to establish probabilistic performance guarantees for parametric optimization problems solved via iterative algorithms. Our approach addresses two key challenges: providing convergence guarantees to…

In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…

We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…

We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…

The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…

In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…

In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…

In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…

Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online…

We explore algorithms and limitations for sparse optimization problems such as sparse linear regression and robust linear regression. The goal of the sparse linear regression problem is to identify a small number of key features, while the…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

Requirements driven search-based testing (also known as falsification) has proven to be a practical and effective method for discovering erroneous behaviors in Cyber-Physical Systems. Despite the constant improvements on the performance and…

This paper initiates the study of I/O algorithms (minimizing cache misses) from the perspective of fine-grained complexity (conditional polynomial lower bounds). Specifically, we aim to answer why sparse graph problems are so hard, and why…

Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…