Stochastic online optimization. Single-point and multi-point non-linear multi-armed bandits. Convex and strongly-convex case

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• 作者：A. V. Gasnikov ; E. A. Krymova ; A. A. Lagunovskaya…
• 关键词：online optimization ; gradient ; free ; inexact oracle ; stochastic optimization
• 刊名：Automation and Remote Control
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：78
• 期：2
• 页码：224-234
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Control, Robotics, Mechatronics; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design;
• 出版者：Pleiades Publishing
• ISSN：1608-3032
• 卷排序：78

文摘

In this paper the gradient-free modification of the mirror descent method for convex stochastic online optimization problems is proposed. The crucial assumption in the problem setting is that function realizations are observed with minor noises. The aim of this paper is to derive the convergence rate of the proposed methods and to determine a noise level which does not significantly affect the convergence rate.