Related papers: Beyond Smoothed Analysis: Analyzing the Simplex Me…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
Empirical studies are fundamental in assessing the effectiveness of implementations of branch-and-bound algorithms. The complexity of such implementations makes empirical study difficult for a wide variety of reasons. Various attempts have…
From self-driving vehicles and back-flipping robots to virtual assistants who book our next appointment at the hair salon or at that restaurant for dinner - machine learning systems are becoming increasingly ubiquitous. The main reason for…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
We describe an efficient implementation of a recent simplex-type algorithm for the exact solution of separated continuous linear programs, and compare it with linear programming approximation of these problems obtained via discretization of…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
Imagine you are a teacher attempting to assess a student's level in a particular subject. If you design a test with only hard questions, and the student fails, this mostly proves that the student does not understand the more advanced…
Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…
Randomized sampling based algorithms are widely used in robot motion planning due to the problem's intractability, and are experimentally effective on a wide range of problem instances. Most variants bias their sampling using various…
Neural algorithmic reasoning is an emerging area of machine learning that focuses on building neural networks capable of solving complex algorithmic tasks. Recent advancements predominantly follow the standard supervised learning paradigm…
In a world of daily emerging scientific inquisition and discovery, the prolific launch of machine learning across industries comes to little surprise for those familiar with the potential of ML. Neither so should the congruent expansion of…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
Randomized smoothing is currently a state-of-the-art method to construct a certifiably robust classifier from neural networks against $\ell_2$-adversarial perturbations. Under the paradigm, the robustness of a classifier is aligned with the…
In designing personalized ranking algorithms, it is desirable to encourage a high precision at the top of the ranked list. Existing methods either seek a smooth convex surrogate for a non-smooth ranking metric or directly modify updating…
We consider a recently introduced framework in which fairness is measured by worst-case outcomes across groups, rather than by the more standard differences between group outcomes. In this framework we provide provably convergent…
The underlying assumption of many machine learning algorithms is that the training data and test data are drawn from the same distributions. However, the assumption is often violated in real world due to the sample selection bias between…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Automated algorithm design is entering a new phase: Large Language Models can now generate full optimisation (meta)heuristics, explore vast design spaces and adapt through iterative feedback. Yet this rapid progress is largely…