Stochastic zeroth order descent with structured directions

Marco Rando (), Cesare Molinari (), Silvia Villa () and Lorenzo Rosasco ()
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Marco Rando: University of Genoa
Cesare Molinari: University of Genoa
Silvia Villa: University of Genoa
Lorenzo Rosasco: University of Genoa

Computational Optimization and Applications, 2024, vol. 89, issue 3, No 5, 727 pages

Abstract: Abstract We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach that approximates a stochastic gradient on a set of $$l\le d$$ l ≤ d orthogonal directions, where d is the dimension of the ambient space. These directions are randomly chosen and may change at each step. For smooth convex functions we prove almost sure convergence of the iterates and a convergence rate on the function values of the form $$O( (d/l) k^{-c})$$ O ( ( d / l ) k - c ) for every $$c

Keywords: Zeroth-order optimization; Finite differences; Black-box optimization; Derivative-free optimization; Stochastic optimization; Convex optimization; 90C56; 90C15; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00616-1

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