Accelerated Alternating Descent Methods for Dykstra-like problems

International audienceThis paper extends recent results by the first author and T. Pock (ICG, TU Graz, Austria) on the acceleration of alternating minimization techniques for quadratic plus nonsmooth objectives depending on two variables. We discuss here the strongly convex situation, and how ‘fast’ methods can be derived by adapting the overrelaxation strategy of Nesterov for projected gradient descent. We also investigate slightly more general alternating descent methods, where several descent steps in each variable are alternatively performed

Free Discontinuity Design: With an Application to the Economic Effects of Internet Shutdowns

Thresholds in treatment assignments can produce discontinuities in outcomes, revealing causal insights. In many contexts, like geographic settings, these thresholds are unknown and multivariate. We propose a non-parametric method to estimate the resulting discontinuities by segmenting the regression surface into smooth and discontinuous parts. This estimator uses a convex relaxation of the Mumford-Shah functional, for which we establish identification and convergence. Using our method, we estimate that an internet shutdown in India resulted in a reduction of economic activity by over 50%, greatly surpassing previous estimates and shedding new light on the true cost of such shutdowns for digital economies globally.Comment: 29 pages, 7 figures; authors listed alphabetically; code available at https://github.com/Davidvandijcke/fd