Related papers: Slide Reduction, Revisited---Filling the Gaps in S…
We study the problem of efficiently summarizing a short video into several keyframes, leveraging recent progress in fast graph sampling. Specifically, we first construct a similarity path graph (SPG) $\mathcal{G}$, represented by graph…
Policy optimization is among the most popular and successful reinforcement learning algorithms, and there is increasing interest in understanding its theoretical guarantees. In this work, we initiate the study of policy optimization for the…
Stein Variational Gradient Descent (SVGD) is an important alternative to the Langevin-type algorithms for sampling from probability distributions of the form $\pi(x) \propto \exp(-V(x))$. In the existing theory of Langevin-type algorithms…
Given a positive integer n and a positive semidefinite matrix A = (A_{ij}) of size m x m, the positive semidefinite Grothendieck problem with rank-n-constraint (SDP_n) is maximize \sum_{i=1}^m \sum_{j=1}^m A_{ij} x_i \cdot x_j, where x_1,…
The Super-SAT or SSAT problem was introduced by Dinur et al.(2002,2003) to prove the NP-hardness of approximation of two popular lattice problems - Shortest Vector Problem(SVP) and Closest Vector Problem(CVP). They conjectured that SSAT is…
For a polygon P with n vertices, the vertex guarding problem asks for the minimum subset G of P's vertices such that every point in P is seen by at least one point in G. This problem is NP-complete and APX-hard. The first approximation…
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…
We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With $O(r^3 \kappa^2 n \log n)$ random…
In his famous book ``Basic Number Theory", Weil proved several theorems about the existence of norm-orthogonal bases in finite-dimensional vector spaces and lattices over local fields. In this paper, we transform Weil's proofs into…
$ \newcommand{\eps}{\varepsilon} \newcommand{\problem}[1]{\ensuremath{\mathrm{#1}} } \newcommand{\CVP}{\problem{CVP}} \newcommand{\SVP}{\problem{SVP}} \newcommand{\CVPP}{\problem{CVPP}} \newcommand{\ensuremath}[1]{#1} $For odd integers $p…
This paper focuses on solving a stochastic variational inequality (SVI) problem under relaxed smoothness assumption for a class of structured non-monotone operators. The SVI problem has attracted significant interest in the machine learning…
We address the problem of model selection for Support Vector Machine (SVM) classification. For fixed functional form of the kernel, model selection amounts to tuning kernel parameters and the slack penalty coefficient $C$. We begin by…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…
We present a unified theorem for the convergence analysis of stochastic gradient algorithms for minimizing a smooth and convex loss plus a convex regularizer. We do this by extending the unified analysis of Gorbunov, Hanzely \& Richt\'arik…
Support vector machines (SVMs) are well-studied supervised learning models for binary classification. In many applications, large amounts of samples can be cheaply and easily obtained. What is often a costly and error-prone process is to…
The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the…
We develop a practical semidefinite programming (SDP) facial reduction procedure that utilizes computationally efficient approximations of the positive semidefinite cone. The proposed method simplifies SDPs with no strictly feasible…
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…