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Zeroth-Order Stochastic Compositional Algorithms for Risk-Aware Learning

We present Free−MESSAGE,p, the first zeroth-order algorithm for (weakly) convex mean-semideviation-based risk-aware learning, which is also the first-ever three-level zeroth-order compositional stochastic optimization algorithm. Using a nontrivial extension of Nesterov's classical results on Gaussian smoothing, we develop the Free−MESSAGE,p algorithm from first principles and show that it essentially solves a smoothed surrogate to the original problem, the former being a uniform approximation of the latter, in a useful, convenient sense. We then present a complete analysis of the Free−MESSAGE,p algorithm, which establishes convergence in a user-tunable neighborhood of the optimal solutions of the original problem for convex costs, as well as explicit convergence rates for convex, weakly convex, and strongly convex costs, in a unified way. Orderwise, and for fixed problem parameters, our results demonstrate no sacrifice in convergence speed as compared to existing first-order methods, while striking a certain balance among the condition of the problem, its dimensionality, and the accuracy of the obtained results, naturally extending previous results in zeroth-order risk-neutral learning.

Ketersediaan

Informasi Detail

Judul Seri

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

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 386-416

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

RISK MEASURES
RISK-AVERSE OPTIMIZATION
STOCHASTIC GRADIENT METHODS
COMPOSITIONAL OPTIMIZATION
RISK-AWARE LEARNING
ZEROTH-ORDER METHODS
MEAN-UPPER-SEMIDEVIATION

Info Detail Spesifik

https://doi.org/10.1137/20M1315403

Pernyataan Tanggungjawab

Dionysios S. Kalogerias, Warren B. Powell

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