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Zeroth-Order Regularized Optimization (ZORO) : Approximately Sparse Gradients and Adaptive Sampling

We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using only (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or black-box optimization. We propose a new zeroth-order regularized optimization method, dubbed ZORO. When the underlying gradient is approximately sparse at an iterate, ZORO needs very few objective function evaluations to obtain a new iterate that decreases the objective function. We achieve this with an adaptive, randomized gradient estimator, followed by an inexact proximal-gradient scheme. Under a novel approximately sparse gradient assumption and various different convex settings, we show that the (theoretical and empirical) convergence rate of ZORO is only logarithmically dependent on the problem dimension. Numerical experiments show that ZORO outperforms existing methods with similar assumptions, on both synthetic and real datasets.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.32 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 687-714

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

DERIVATIVE-FREE OPTIMIZATION
REGULARIZED OPTIMIZATION
BLACK-BOX OPTIMIZATION
ZEROTH-ORDER OPTIMIZATION
SPARSE GRADIENTS
SPARSE ADVERSARIAL ATTACK

Info Detail Spesifik

https://doi.org/10.1137/21M1392966

Pernyataan Tanggungjawab

HanQin Cai, Daniel McKenzie, Wotao Yin, Zhenliang Zhang

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