Mini-batch Stochastic Subgradient for Functional Constrained Optimization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00365965" target="_blank" >RIV/68407700:21230/24:00365965 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1080/02331934.2023.2189015" target="_blank" >https://doi.org/10.1080/02331934.2023.2189015</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/02331934.2023.2189015" target="_blank" >10.1080/02331934.2023.2189015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Mini-batch Stochastic Subgradient for Functional Constrained Optimization

Popis výsledku v původním jazyce

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1-35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart.

Název v anglickém jazyce

Mini-batch Stochastic Subgradient for Functional Constrained Optimization

Popis výsledku anglicky

In this paper, we consider finite sum composite optimization problems with many functional constraints. The objective function is expressed as a finite sum of two terms, one of which admits easy computation of (sub)gradients while the other is amenable to proximal evaluations. We assume a generalized bounded gradient condition on the objective which allows us to simultaneously tackle both smooth and nonsmooth problems. We also consider the cases of both with and without a quadratic functional growth property. Further, we assume that each constraint set is given as the level set of a convex but not necessarily a differentiable function. We reformulate the constrained finite sum problem into a stochastic optimization problem for which the stochastic subgradient projection method from Necoara and Singh [Stochastic subgradient projection methods for composite optimization with functional constraints; 2022 Journal of Machine Learning Research, 23, 1-35] specializes in a collection of mini-batch variants, with different mini-batch sizes for the objective function and functional constraints, respectively. More specifically, at each iteration, our algorithm takes a mini-batch stochastic proximal subgradient step aimed at minimizing the objective function and then a subsequent mini-batch subgradient projection step minimizing the feasibility violation. By specializing in different mini-batching strategies, we derive exact expressions for the stepsizes as a function of the mini-batch size and in some cases we also derive insightful stepsize-switching rules which describe when one should switch from a constant to a decreasing stepsize regime. We also prove sublinear convergence rates for the mini-batch subgradient projection algorithm which depend explicitly on the mini-batch sizes and on the properties of the objective function. Numerical results also show a better performance of our mini-batch scheme over its single-batch counterpart.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/EF16_019%2F0000765" target="_blank" >EF16_019/0000765: Výzkumné centrum informatiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Optimization

ISSN

0233-1934

e-ISSN

1029-4945

Svazek periodika

73

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

27

Strana od-do

2159-2185

Kód UT WoS článku

000950116300001

EID výsledku v databázi Scopus

2-s2.0-85149908573