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Sujets
Informations
Publié par | pefav |
Nombre de lectures | 12 |
Langue | English |
Poids de l'ouvrage | 1 Mo |
Extrait
July2011
2
INRIA/ENS
1
UniversityofBritishColumbia
MichaelFriedlander
1
MarkSchmidt
2
HybridDeterministic-StochasticMethodsforData
Fitting
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteD
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMOtherProjectsandSummary
4
PracticalIssuesandApplication
y3
rConvergenceRatesofGradientMethods
a2
m1
mDeterministicvs.StochasticOptimization
uOutline
SdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteD
naseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteDShouldweuse
AlgorithmS
or
AlgorithmD
?
AlgorithmSvs.AlgorithmD:
Errorvs.Iteration
H
Al
y
g
b
o
ri
ri
d
th
M
m
et
S
ho
vs
d
.
s
AlgorithmD
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciM.k2/1fororrenasahDmhtiroglA,knoitaretinO.k/1fororrenasahSmhtiroglA,knoitaretinOyrammuSdnastcejorPrehtOnoitacilppAd
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMShouldweuse
AlgorithmS
or
AlgorithmD
?
Oniteration
k
,
AlgorithmS
hasanerrorof1
/
k
.
Oniteration
k
,
AlgorithmD
hasanerrorof1
/
2
k
.
sAlgorithmSvs.AlgorithmD:Errorvs.Iteration
dohteMdirbyHDmhtiroglA.svSmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteD
arGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteDShouldweuse
AlgorithmS
or
AlgorithmD
?
Oniteration
k
,
AlgorithmS
hasanerrorof1
/
k
.
Oniteration
k
,
AlgorithmD
hasanerrorof1
/
2
k
.
AlgorithmSvs.AlgorithmD:Errorvs.Iteration
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMsdohteMdirbyHDmhtiroglA.svSmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneid
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciM.evisnepxeeraDmhtiroglAfosnoitaretI.paehceraSmhtiroglAfosnoitaretIsdohteMdirbyHDmhtiroglA.sBut,theerrorisnotthewholestory:
vAlgorithmSvs.AlgorithmD:Errorvs.Time
SmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteD
aRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteDBut,theerrorisnotthewholestory:
Iterationsof
AlgorithmD
are
expensive
.
Iterationsof
AlgorithmS
are
cheap
.
AlgorithmSvs.AlgorithmD:Errorvs.Time
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMsdohteMdirbyHDmhtiroglA.svSmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfoset
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMsdohBut,theerrorisnotthewholestory:
tIterationsof
AlgorithmD
are
expensive
.
eIterationsof
AlgorithmS
are
cheap
.
MAlgorithmSvs.AlgorithmD:Errorvs.Time
dirbyHDmhtiroglA.svSmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteD
tneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteDDeterminstic
makessteadyprogress,butisexpensive.
Stochastic
makesgreatprogressinitially,butslowsdown.
Stochasticvs.Deterministic:
MotivationforHybridMethods
gnittiFataDrofsdohteMcitsahcotS-citsinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciM?sdlrowhtobfotsebehttegdohtemdirbyhanaCsdohteMdirbyHDmhtiroglA.svSmhtiroglAyrammuSdnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteM
sinimreteDdirbyHtidmhcSkraMdnarednaldeirFleahciMsdohteMdirbyHDmhtiroglA.svSmhtiroglAyraCana
hybrid
methodgetthebestofbothworlds?
mDeterminstic
makessteadyprogress,butisexpensive.
mStochastic
makesgreatprogressinitially,butslowsdown.
uStochasticvs.Deterministic:
SMotivationforHybridMethods
dnastcejorPrehtOnoitacilppAdnaseussIlacitcarPsdohteMtneidarGfosetaRecnegrevnoCnoitazimitpOcitsahcotS.svcitsinimreteDgnittiFataDrofsdohteMcitsahcotS-cit