<s>
Simultaneous	B-Algorithm
perturbation	I-Algorithm
stochastic	I-Algorithm
approximation	I-Algorithm
(	O
SPSA	O
)	O
is	O
an	O
algorithmic	O
method	O
for	O
optimizing	O
systems	O
with	O
multiple	O
unknown	O
parameters	O
.	O
</s>
<s>
SPSA	O
is	O
a	O
descent	O
method	O
capable	O
of	O
finding	O
global	O
minima	O
,	O
sharing	O
this	O
property	O
with	O
other	O
methods	O
as	O
simulated	B-Algorithm
annealing	I-Algorithm
.	O
</s>
<s>
If	O
is	O
a	O
p-dimensional	O
vector	O
,	O
the	O
component	O
of	O
the	O
symmetric	B-Algorithm
finite	O
difference	O
gradient	O
estimator	O
is	O
:	O
</s>
<s>
Simple	O
experiments	O
with	O
p	O
=	O
2	O
showed	O
that	O
SPSA	O
converges	B-Algorithm
in	O
the	O
same	O
number	O
of	O
iterations	O
as	O
FDSA	O
.	O
</s>
<s>
Next	O
we	O
resume	O
some	O
of	O
the	O
hypotheses	O
under	O
which	O
converges	B-Algorithm
in	O
probability	O
to	O
the	O
set	O
of	O
global	O
minima	O
of	O
.	O
</s>
<s>
Under	O
these	O
conditions	O
and	O
a	O
few	O
others	O
,	O
converges	B-Algorithm
in	O
probability	O
to	O
the	O
set	O
of	O
global	O
minima	O
of	O
J(u )	O
(	O
see	O
Maryak	O
and	O
Chin	O
,	O
2008	O
)	O
.	O
</s>
<s>
It	O
has	O
been	O
shown	O
that	O
differentiability	O
is	O
not	O
required	O
:	O
continuity	O
and	O
convexity	O
are	O
sufficient	O
for	O
convergence	B-Algorithm
.	O
</s>
<s>
As	O
with	O
the	O
basic	O
SPSA	O
method	O
,	O
only	O
a	O
small	O
fixed	O
number	O
of	O
loss	O
measurements	O
or	O
gradient	O
measurements	O
are	O
needed	O
at	O
each	O
iteration	O
,	O
regardless	O
of	O
the	O
problem	O
dimension	O
p	O
.	O
See	O
the	O
brief	O
discussion	O
in	O
Stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
.	O
</s>
