Stochastic variance-reduced prox-linear algorithms for nonconvex composite optimization
We consider the problem of minimizing composite functions of the form f ( g ( x ) ) + h ( x ) , where f and h are convex functions (which can be nonsmooth) and g is a smooth vector mapping. In addition, we assume that g is the average of finite number of component mappings or the expectation over...
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| Veröffentlicht in: | Mathematical programming Jg. 195; H. 1-2; S. 649 - 691 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2022
Springer Springer Nature B.V |
| Schlagworte: | |
| ISSN: | 0025-5610, 1436-4646 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We consider the problem of minimizing composite functions of the form
f
(
g
(
x
)
)
+
h
(
x
)
, where
f
and
h
are convex functions (which can be nonsmooth) and
g
is a smooth vector mapping. In addition, we assume that
g
is the average of finite number of component mappings or the expectation over a family of random component mappings. We propose a class of stochastic variance-reduced prox-linear algorithms for solving such problems and bound their sample complexities for finding an
ϵ
-stationary point in terms of the total number of evaluations of the component mappings and their Jacobians. When
g
is a finite average of
N
components, we obtain sample complexity
O
(
N
+
N
4
/
5
ϵ
-
1
)
for both mapping and Jacobian evaluations. When
g
is a general expectation, we obtain sample complexities of
O
(
ϵ
-
5
/
2
)
and
O
(
ϵ
-
3
/
2
)
for component mappings and their Jacobians respectively. If in addition
f
is smooth, then improved sample complexities of
O
(
N
+
N
1
/
2
ϵ
-
1
)
and
O
(
ϵ
-
3
/
2
)
are derived for
g
being a finite average and a general expectation respectively, for both component mapping and Jacobian evaluations. |
|---|---|
| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0025-5610 1436-4646 |
| DOI: | 10.1007/s10107-021-01709-z |