<s>
In	O
mathematics	O
,	O
mirror	B-Algorithm
descent	I-Algorithm
is	O
an	O
iterative	B-Algorithm
optimization	O
algorithm	O
for	O
finding	O
a	O
local	O
minimum	O
of	O
a	O
differentiable	O
function	O
.	O
</s>
<s>
It	O
generalizes	O
algorithms	O
such	O
as	O
gradient	B-Algorithm
descent	I-Algorithm
and	O
multiplicative	B-Algorithm
weights	I-Algorithm
.	O
</s>
<s>
Mirror	B-Algorithm
descent	I-Algorithm
was	O
originally	O
proposed	O
by	O
Nemirovski	O
and	O
Yudin	O
in	O
1983	O
.	O
</s>
<s>
This	O
Euclidean	O
distance	O
term	O
is	O
a	O
particular	O
example	O
of	O
a	O
Bregman	B-Algorithm
distance	I-Algorithm
.	O
</s>
<s>
Using	O
other	O
Bregman	B-Algorithm
distances	I-Algorithm
will	O
yield	O
other	O
algorithms	O
such	O
as	O
Hedge	B-Algorithm
which	O
may	O
be	O
more	O
suited	O
to	O
optimization	O
over	O
particular	O
geometries	O
.	O
</s>
<s>
Starting	O
from	O
initial	O
,	O
in	O
each	O
iteration	O
of	O
Mirror	B-Algorithm
Descent	I-Algorithm
:	O
</s>
<s>
Project	O
back	O
to	O
the	O
feasible	O
region	O
:	O
,	O
where	O
is	O
the	O
Bregman	B-Algorithm
divergence	I-Algorithm
.	O
</s>
<s>
Mirror	B-Algorithm
descent	I-Algorithm
in	O
the	O
online	B-Algorithm
optimization	I-Algorithm
setting	O
is	O
known	O
as	O
Online	B-Algorithm
Mirror	I-Algorithm
Descent	I-Algorithm
(	O
OMD	O
)	O
.	O
</s>
