NIPS Proceedingsβ

Zeroth-order (Non)-Convex Stochastic Optimization via Conditional Gradient and Gradient Updates

Part of: Advances in Neural Information Processing Systems 31 (NIPS 2018) pre-proceedings

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Authors

Conference Event Type: Poster

Abstract

In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization. Specifically, we propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. Furthermore, under a structural sparsity assumption, we first illustrate an implicit regularization phenomenon where the standard stochastic gradient algorithm with zeroth-order information adapts to the sparsity of the problem at hand by just varying the step-size. Next, we propose a truncated stochastic gradient algorithm with zeroth-order information, whose rate of convergence depends only poly-logarithmically on the dimensionality.