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We study approximation of multivariate functions from a separable Hilbert space in the randomized setting with the error measured in the weighted $L_2$ norm. We consider algorithms that use standard information $\Lambda^{\rm std}$…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
Sparsity constrained minimization captures a wide spectrum of applications in both machine learning and signal processing. This class of problems is difficult to solve since it is NP-hard and existing solutions are primarily based on…
In this paper, we propose a novel feature weighting method to address the limitation of existing feature processing methods for tabular data. Typically the existing methods assume equal importance across all samples and features in one…
We study multivariate approximation in the average case setting with the error measured in the weighted $L_2$ norm. We consider algorithms that use standard information $\Lambda^{\rm std}$ consisting of function values or general linear…
The target discounted-sum problem is the following: Given a rational discount factor $0<\lambda<1$ and three rational values $a,b$, and $t$, does there exist a finite or an infinite sequence $w \in \{a,b\}^*$ or $w \in \{a,b\}^\omega$, such…
We introduce a novel multivariate approach for solving weighted parameterized problems. In our model, given an instance of size $n$ of a minimization (maximization) problem, and a parameter $W \geq 1$, we seek a solution of weight at most…
This paper investigates the convexity of the solution set of the linear complementarity problems over tensor spaces (TLCPs). We introduce the notion of a $T$-column sufficient tensor and study its properties and relationships with several…
This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…
This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…
In this paper we deal with infinite horizon optimal control problems. Basing on weak variations in an extremal problem in weighted function spaces we prove necessary conditions in form of the adjoint equation and a variational inequality.…
Finding the sparsest solutions to a tensor complementarity problem is generally NP-hard due to the nonconvexity and noncontinuity of the involved $\ell_0$ norm. In this paper, a special type of tensor complementarity problems with…
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate…
We start with a stochastic control problem where the control process is of finite variation (possibly with jumps) and acts as integrator both in the state dynamics and in the target functional. Problems of such type arise in the stream of…
We study least-squares trace regression when the parameter is the sum of a $r$-low-rank matrix and a $s$-sparse matrix and a fraction $\epsilon$ of the labels is corrupted. For subgaussian distributions and feature-dependent noise, we…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
We study the optimal contract problem in the \emph{combinatorial actions} framework of D\"utting et al.~[FOCS'21], where a principal delegates a project to an agent who chooses a subset of hidden, costly actions, and the resulting reward is…
In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these…