In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

We consider a multidimensional search problem that is motivated by questions in contextual decision-making, such as dynamic pricing and personalized medicine. Nature selects a state from a d-dimensional unit ball and then generates a sequence of d-dimensional directions. We are given access to the directions, but not access to the state. After receiving a direction, we have to guess the value of the dot product between the state and the direction. Our goal is to minimize the number of times when our guess is more than o away from the true answer. We construct a polynomial time algorithm that we call Projected Volume achieving regret O(d log(d/o)), which is optimal up to a log d factor. The algorithm combines a volume cutting strategy with a new geometric technique that we call cylindrification.
Multidimensional Binary Search for Contextual Decision-Making

An emerging way to deal with highdimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.
A Time-Vertex Signal Processing Framework Scalable processing and meaningful representations for time-series on graphs

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of N nonconvex Li/N -smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into N subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves -stationary solution using O(( N i=1 Li/N) / ) gradient evaluations, which can be up to O(N) times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex '1 penalized quadratic problems with polyhedral constraints. Further, we reveal a fundamental connection between primal-dual based methods and a few primal only methods such as IAG/SAG/SAGA.
NESTT: A Nonconvex Primal-Dual Splitting Method for Distributed and Stochastic Optimization