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Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Nonconvex Stochastic Optimization : Nonasymptotic Performance Bounds and Momentum-Based Acceleration

Stochastic gradient Hamiltonian Monte Carlo (SGHMC) is a variant of stochastic gradients with momentum where a controlled and properly scaled Gaussian noise is added to the stochastic gradients to steer the iterates toward a global minimum. Many works report its empirical success in practice for solving stochastic nonconvex optimization problems; in particular, it has been observed to outperform overdamped Langevin Monte Carlo–based methods, such as stochastic gradient Langevin dynamics (SGLD), in many applications. Although the asymptotic global convergence properties of SGHMC are well known, its finite-time performance is not well understood. In this work, we study two variants of SGHMC based on two alternative discretizations of the underdamped Langevin diffusion. We provide finite-time performance bounds for the global convergence of both SGHMC variants for solving stochastic nonconvex optimization problems with explicit constants. Our results lead to nonasymptotic guarantees for both population and empirical risk minimization problems. For a fixed target accuracy level on a class of nonconvex problems, we obtain complexity bounds for SGHMC that can be tighter than those available for SGLD.

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Informasi Detail

Judul Seri

OPERATIONS RESEARCH; Vol.70 No.5 September-October 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2931-2947

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

GIBBS SAMPLING
EMPIRICAL RISK MINIMIZATION
NONCONVEX OPTIMIZATION
LANGEVIN DYNAMICS
STOCHASTIC GRADIENT METHODS
MOMENTUM-BASED ACCELERATION

Info Detail Spesifik

https://doi.org/10.1287/opre.2021.2162

Pernyataan Tanggungjawab

Xuefeng Gao, Mert Gürbüzbalaban, Lingjiong Zhu

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