Accelerated Extra-Gradient Descent: A Novel Accelerated First-Order Method
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We provide a novel accelerated first-order method that achieves the asymptotically optimal convergence rate for smooth functions in the first-order oracle model. To this day, Nesterov's Accelerated Gradient Descent (AGD) and variations thereof were the only methods achieving acceleration in this standard blackbox model. In contrast, our algorithm is significantly different from AGD, as it relies on a predictor-corrector approach similar to that used by Mirror-Prox and Extra-Gradient Descent in the solution of convex-concave saddle point problems. For this reason, we dub our algorithm Accelerated Extra-Gradient Descent (AXGD). Its construction is motivated by the discretization of an accelerated continuous-time dynamics using the classical method of implicit Euler discretization. Our analysis explicitly shows the effects of discretization through a conceptually novel primal-dual viewpoint. Finally, we present experiments showing that our algorithm matches the performance of Nesterov's method, while appearing more robust to noise in some cases.
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