Related papers: Fast Subspace Approximation via Greedy Least-Squar…

Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier,…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important…

Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…

We study the min-max optimization problem where each function contributing to the max operation is strongly-convex and smooth with bounded gradient in the search domain. By smoothing the max operator, we show the ability to achieve an…

This paper is motivated by recent research in the $d$-dimensional stochastic linear bandit literature, which has revealed an unsettling discrepancy: algorithms like Thompson sampling and Greedy demonstrate promising empirical performance,…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…

In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function,…

Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

Data-driven decision-making is performed by solving a parameterized optimization problem, and the optimal decision is given by an optimal solution for unknown true parameters. We often need a solution that satisfies true constraints even…

This paper addresses the problem of learning to sparsify stochastic linear bandits, where a decision-maker sequentially selects actions from a high-dimensional space subject to a sparsity constraint on the number of nonzero elements in the…

Let $X$ be a set of $n$ points of norm at most $1$ in the Euclidean space $R^k$, and suppose $\varepsilon>0$. An $\varepsilon$-distance sketch for $X$ is a data structure that, given any two points of $X$ enables one to recover the square…

Reduced model spaces, such as reduced basis and polynomial chaos, are linear spaces $V_n$ of finite dimension $n$ which are designed for the efficient approximation of families parametrized PDEs in a Hilbert space $V$. The manifold…

Good approximations have been attained for the sparsest cut problem by rounding solutions to convex relaxations via low-distortion metric embeddings. Recently, Bryant and Tupper showed that this approach extends to the hypergraph setting by…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for $n$ data points requires $\Omega(n^2)$ similarity computations. This quadratic…

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth…

In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…