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Two directions in algorithms and complexity involve: (1) classifying which optimization problems can be solved in polynomial time, and (2) understanding which computational problems are hard to solve \emph{on average} in addition to the…
We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated…
Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the…
In this paper, we consider the problem of preserving privacy in the online learning setting. We study the problem in the online convex programming (OCP) framework---a popular online learning setting with several interesting theoretical and…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
Set cover and hitting set are fundamental problems in combinatorial optimization which are well-studied in the offline, online, and dynamic settings. We study the geometric versions of these problems and present new online and dynamic…
Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…
In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…
We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or Ising $p$-spin glass model, and (b)…
Metric embeddings into structured spaces, particularly hierarchically well-separated trees (HSTs), are a fundamental tool in the design of online algorithms. In the classical online embedding setting, points arrive sequentially and must be…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
This non-conventional paper represents the first attempt to uncover a possible vulnerability in some proposals for optical network designs and performance comparisons. While optical network designs and planning lie at the heart of achieving…
Online algorithms with predictions is a popular and elegant framework for bypassing pessimistic lower bounds in competitive analysis. In this model, online algorithms are supplied with future predictions, and the goal is for the competitive…
We consider online packing problems where we get a stream of axis-parallel rectangles. The rectangles have to be placed in the plane without overlapping, and each rectangle must be placed without knowing the subsequent rectangles. The goal…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear convex Euler-Lagrange equations. This class of problems includes many highly nonlinear partial differential equations, such as $p$-Laplacians. We prove that, if…
In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…
Online mirror descent (OMD) is a fundamental algorithmic paradigm that underlies many algorithms in optimization, machine learning and sequential decision-making. The OMD iterates are defined as solutions to optimization subproblems which,…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of…
We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…