We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using only noisy evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or black-box optimization. We propose a new Zeroth-Order Regularized Optimization method, dubbed ZORO. When the underlying gradient is approximately sparse at an iterate, ZORO needs very few objective function evaluations to obtain a new iterate that decreases the objective function. We achieve this with an adaptive, randomized gradient estimator, followed by an inexact proximal-gradient scheme. Under a novel approximately sparse gradient assumption and various different convex settings, we show the (theoretical and empirical) convergence rate of ZORO is only logarithmically dependent on the problem dimension. Numerical experiments show ZORO outperforms existing methods on both synthetic and real datasets.

As a good battle shonen should, One Piece has a variety of iconic fights that are complemented by some flashy and exciting finishing moves. A staple of any anime fight, the idea of the finishing move fuses both brutal power and explicit branding to create some of the most exciting and recognizable attacks ever seen in fiction. In One Piece's world, Devil Fruits, Haki, martial arts, robotic enhancements, and some very loose interpretations of physics all contribute to One Piece's own, colorful gallery of finishing moves. And while rating each one's power and effectiveness is a large discussion within its own right, it's also really fun just looking at which finishing moves are just the coolest and most memorable. Monkey D. Luffy's Gum-Gum Gatling doesn't have the awe-inspiring, simplistic appeal of a one-hit attack; but what it lacks in brevity, it more than makes up for with raw, visceral spectacle.