Related papers: Variable Decomposition for Prophet Inequalities an…
We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
We study the multivariate nonparametric change point detection problem, where the data are a sequence of independent $p$-dimensional random vectors whose distributions are piecewise-constant with Lipschitz densities changing at unknown…
In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
The study of the prophet inequality problem in the limited information regime was initiated by Azar et al. [SODA'14] in the pursuit of prior-independent posted-price mechanisms. As they show, $O(1)$-competitive policies are achievable using…
In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…
Competition complexity formalizes a compelling intuition: rather than refining the mechanism, how much additional competition is sufficient for a simple mechanism to compete with an optimal one? We begin the study of this question in…
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $n \Delta$ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, $n$ is the…
We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
At each iteration of a Block Coordinate Descent method one minimizes an approximation of the objective function with respect to a generally small set of variables subject to constraints in which these variables are involved. The…
We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…