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Randomized Derivative-Free Optimization of Noisy Convex Functions

Ruobing Chen(ruobing.chen***at***us.bosch.com)
Stefan Wild(wild***at***mcs.anl.gov)

Abstract: We propose STARS, a randomized derivative-free algorithm for unconstrained optimization when the function evaluations are contaminated with random noise. STARS takes dynamic, noise-adjusted smoothing step-sizes that minimize the least-squares error between the true directional derivative of a noisy function and its finite difference approximation. We provide a convergence rate analysis of STARS for solving convex problems with additive or multiplicative noise. Experimental results show that (1) STARS exhibits noise-invariant behavior with respect to different levels of stochastic noise; (2) the practical performance of STARS in terms of solution accuracy and convergence rate is significantly better than that indicated by the theoretical result; and (3) STARS outperforms a selection of randomized zero-order methods on both additive and multiplicative-noisy functions.

Keywords: derivative-free optimization, randomized search, random noisy, convex function

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Stochastic Programming


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Entry Submitted: 07/13/2015
Entry Accepted: 07/13/2015
Entry Last Modified: 07/13/2015

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