Related papers: Minimax optimal seriation in polynomial time
We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
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…
Seriation methods order a set of descriptions given some criterion (e.g., unimodality or minimum distance between similarity scores). Seriation is thus inherently a problem of finding the optimal solution among a set of permutations of…
We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax…
We study a class of polynomial optimization problems with a robust polynomial matrix inequality (PMI) constraint where the uncertainty set itself is defined also by a PMI. These can be viewed as matrix generalizations of semi-infinite…
We study the problem of aggregating polygons by covering them with disjoint representative regions, thereby inducing a clustering of the polygons. Our objective is to minimize a weighted sum of the total area and the total perimeter of the…
The Landau-Lifshitz equation is the first in an infinite series of approximations to the Lorentz-Abraham-Dirac equation obtained from `reduction of order'. We show that this series is divergent, predicting wildly different dynamics at…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
We study a submodular maximization problem motivated by applications in online retail. A platform displays a list of products to a user in response to a search query. The user inspects the first $k$ items in the list for a $k$ chosen at…
We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum…
Many important multiple-objective decision problems can be cast within the framework of ranking under constraints and solved via a weighted bipartite matching linear program. Some of these optimization problems, such as personalized content…
Mining and exploring databases should provide users with knowledge and new insights. Tiles of data strive to unveil true underlying structure and distinguish valuable information from various kinds of noise. We propose a novel Boolean…
In this paper, we leverage an information-theoretic upper bound on the maximum admissible level of noise (MALN) in convex Lipschitz-continuous zeroth-order optimisation to establish corresponding upper bounds for classes of strongly convex…
We consider the problem of structured tensor denoising in the presence of unknown permutations. Such data problems arise commonly in recommendation system, neuroimaging, community detection, and multiway comparison applications. Here, we…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…