Related papers: The Bit Complexity of Efficient Continuous Optimiz…
We consider the problem of the computation of $\inf_p \theta p$ over the set of exponent pairs $P \ni p$ under linear constraints for a certain class of objective functions $\theta$. An effective algorithm is presented. The output of the…
This technical note extends recent results on the computational complexity of globally minimizing the error of piecewise-affine models to the related problem of minimizing the error of switching linear regression models. In particular, we…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
Data-driven inverse optimization for mixed-integer linear programs (MILPs), which seeks to learn an objective function and constraints consistent with observed decisions, is important for building accurate mathematical models in a variety…
The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while…
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include…
In this paper we obtain improved iteration complexities for solving $\ell_p$ regression. We provide methods which given any full-rank $\mathbf{A} \in \mathbb{R}^{n \times d}$ with $n \geq d$, $b \in \mathbb{R}^n$, and $p \geq 2$ solve…
The deployment constraints in practical applications necessitate the pruning of large-scale deep learning models, i.e., promoting their weight sparsity. As illustrated by the Lottery Ticket Hypothesis (LTH), pruning also has the potential…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is…
We consider the online sparse linear regression problem, which is the problem of sequentially making predictions observing only a limited number of features in each round, to minimize regret with respect to the best sparse linear regressor,…
We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…
We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times…
Computational equilibrium finding in large zero-sum extensive-form imperfect-information games has led to significant recent AI breakthroughs. The fastest algorithms for the problem are new forms of counterfactual regret minimization [Brown…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
The linearly constrained matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. The tightest convex relaxation of this problem is the linearly constrained nuclear…