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Author: Gasnikov, Alexander × Subject: first-order method ×

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    Adaptive gradient descent for convex and non-convex stochastic optimization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Ogaltsov, Aleksandr; Dvinskikh, Darina; Dvurechensky, Pavel; Gasnikov, Alexander; Spokoiny, Vladimir
    In this paper we propose several adaptive gradient methods for stochastic optimization. Our methods are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of the gradient and variance of the stochastic approximation for the gradient. We consider an accelerated gradient descent for convex problems and gradient descent for non-convex problems. In the experiments we demonstrate superiority of our methods to existing adaptive methods, e.g. AdaGrad and Adam.
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    On primal and dual approaches for distributed stochastic convex optimization over networks
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Dvinskikh, Darina; Gorbunov, Eduard; Gasnikov, Alexander; Dvurechensky, Alexander; Uribe, César A.
    We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis method for the rate of convergence in terms of duality gap and probability of large deviations. This analysis is based on a new technique that allows to bound the distance between the iteration sequence and the optimal point. By the proper choice of batch size, we can guarantee that this distance equals (up to a constant) to the distance between the starting point and the solution.