<s>
AlphaZero	B-Application
is	O
a	O
computer	B-Application
program	I-Application
developed	O
by	O
artificial	B-Application
intelligence	I-Application
research	I-Application
company	O
DeepMind	B-Application
to	O
master	O
the	O
games	O
of	O
chess	B-Application
,	O
shogi	O
and	O
go	O
.	O
</s>
<s>
This	O
algorithm	O
uses	O
an	O
approach	O
similar	O
to	O
AlphaGo	B-Application
Zero	I-Application
.	O
</s>
<s>
On	O
December	O
5	O
,	O
2017	O
,	O
the	O
DeepMind	B-Application
team	O
released	O
a	O
preprint	O
paper	O
introducing	O
AlphaZero	B-Application
,	O
which	O
within	O
24	O
hours	O
of	O
training	O
achieved	O
a	O
superhuman	O
level	O
of	O
play	O
in	O
these	O
three	O
games	O
by	O
defeating	O
world-champion	O
programs	O
Stockfish	B-Application
,	O
Elmo	B-Application
,	O
and	O
the	O
three-day	O
version	O
of	O
AlphaGo	B-Application
Zero	I-Application
.	O
</s>
<s>
In	O
each	O
case	O
it	O
made	O
use	O
of	O
custom	O
tensor	B-Device
processing	I-Device
units	I-Device
(	O
TPUs	O
)	O
that	O
the	O
Google	O
programs	O
were	O
optimized	O
to	O
use	O
.	O
</s>
<s>
AlphaZero	B-Application
was	O
trained	O
solely	O
via	O
self-play	B-Algorithm
using	O
5,000	O
first-generation	O
TPUs	O
to	O
generate	O
the	O
games	O
and	O
64	O
second-generation	O
TPUs	O
to	O
train	O
the	O
neural	B-Architecture
networks	I-Architecture
,	O
all	O
in	O
parallel	B-Operating_System
,	O
with	O
no	O
access	O
to	O
opening	O
books	O
or	O
endgame	O
tables	O
.	O
</s>
<s>
After	O
four	O
hours	O
of	O
training	O
,	O
DeepMind	B-Application
estimated	O
AlphaZero	B-Application
was	O
playing	O
chess	B-Application
at	O
a	O
higher	O
Elo	O
rating	O
than	O
Stockfish	B-Application
8	O
;	O
after	O
nine	O
hours	O
of	O
training	O
,	O
the	O
algorithm	O
defeated	O
Stockfish	B-Application
8	O
in	O
a	O
time-controlled	O
100-game	O
tournament	O
(	O
28	O
wins	O
,	O
0	O
losses	O
,	O
and	O
72	O
draws	O
)	O
.	O
</s>
<s>
DeepMind	B-Application
's	O
paper	O
on	O
AlphaZero	B-Application
was	O
published	O
in	O
the	O
journal	O
Science	O
on	O
7	O
December	O
2018	O
;	O
however	O
,	O
the	O
AlphaZero	B-Application
program	O
itself	O
has	O
not	O
been	O
made	O
available	O
to	O
the	O
public	O
.	O
</s>
<s>
In	O
2019	O
,	O
DeepMind	B-Application
published	O
a	O
new	O
paper	O
detailing	O
MuZero	B-Application
,	O
a	O
new	O
algorithm	O
able	O
to	O
generalise	O
AlphaZero	B-Application
's	O
work	O
,	O
playing	O
both	O
Atari	B-General_Concept
and	O
board	O
games	O
without	O
knowledge	O
of	O
the	O
rules	O
or	O
representations	O
of	O
the	O
game	O
.	O
</s>
<s>
AlphaZero	B-Application
(	O
AZ	O
)	O
is	O
a	O
more	O
generalized	O
variant	O
of	O
the	O
AlphaGo	B-Application
Zero	I-Application
(	O
AGZ	O
)	O
algorithm	O
,	O
and	O
is	O
able	O
to	O
play	O
shogi	O
and	O
chess	B-Application
as	O
well	O
as	O
Go	O
.	O
</s>
<s>
AZ	O
has	O
hard-coded	O
rules	O
for	O
setting	O
search	O
hyperparameters	B-General_Concept
.	O
</s>
<s>
The	O
neural	B-Architecture
network	I-Architecture
is	O
now	O
updated	O
continually	O
.	O
</s>
<s>
Chess	B-Application
can	O
end	O
in	O
a	O
draw	O
unlike	O
Go	O
;	O
therefore	O
,	O
AlphaZero	B-Application
takes	O
into	O
account	O
the	O
possibility	O
of	O
a	O
drawn	O
game	O
.	O
</s>
<s>
Comparing	O
Monte	B-Application
Carlo	I-Application
tree	I-Application
search	I-Application
searches	O
,	O
AlphaZero	B-Application
searches	O
just	O
80,000	O
positions	O
per	O
second	O
in	O
chess	B-Application
and	O
40,000	O
in	O
shogi	O
,	O
compared	O
to	O
70	O
million	O
for	O
Stockfish	B-Application
and	O
35	O
million	O
for	O
Elmo	B-Application
.	O
</s>
<s>
AlphaZero	B-Application
compensates	O
for	O
the	O
lower	O
number	O
of	O
evaluations	O
by	O
using	O
its	O
deep	O
neural	B-Architecture
network	I-Architecture
to	O
focus	O
much	O
more	O
selectively	O
on	O
the	O
most	O
promising	O
variation	O
.	O
</s>
<s>
AlphaZero	B-Application
was	O
trained	O
solely	O
via	O
self-play	B-Algorithm
,	O
using	O
5,000	O
first-generation	O
TPUs	O
to	O
generate	O
the	O
games	O
and	O
64	O
second-generation	O
TPUs	O
to	O
train	O
the	O
neural	B-Architecture
networks	I-Architecture
.	O
</s>
<s>
In	O
parallel	B-Operating_System
,	O
the	O
in-training	O
AlphaZero	B-Application
was	O
periodically	O
matched	O
against	O
its	O
benchmark	O
(	O
Stockfish	B-Application
,	O
Elmo	B-Application
,	O
or	O
AlphaGo	B-Application
Zero	I-Application
)	O
in	O
brief	O
one-second-per-move	O
games	O
to	O
determine	O
how	O
well	O
the	O
training	O
was	O
progressing	O
.	O
</s>
<s>
DeepMind	B-Application
judged	O
that	O
AlphaZero	B-Application
's	O
performance	O
exceeded	O
the	O
benchmark	O
after	O
around	O
four	O
hours	O
of	O
training	O
for	O
Stockfish	B-Application
,	O
two	O
hours	O
for	O
Elmo	B-Application
,	O
and	O
eight	O
hours	O
for	O
AlphaGo	B-Application
Zero	I-Application
.	O
</s>
<s>
In	O
AlphaZero	B-Application
's	O
chess	B-Application
match	O
against	O
Stockfish	B-Application
8	O
(	O
2016	O
TCEC	O
world	O
champion	O
)	O
,	O
each	O
program	O
was	O
given	O
one	O
minute	O
per	O
move	O
.	O
</s>
<s>
AlphaZero	B-Application
was	O
flying	O
the	O
English	O
flag	O
,	O
while	O
Stockfish	B-Application
the	O
Norwegian	O
.	O
</s>
<s>
Stockfish	B-Application
was	O
allocated	O
64	O
threads	O
and	O
a	O
hash	B-Algorithm
size	O
of	O
1	O
GB	O
,	O
a	O
setting	O
that	O
Stockfish	B-Application
's	O
Tord	O
Romstad	O
later	O
criticized	O
as	O
suboptimal	O
.	O
</s>
<s>
AlphaZero	B-Application
was	O
trained	O
on	O
chess	B-Application
for	O
a	O
total	O
of	O
nine	O
hours	O
before	O
the	O
match	O
.	O
</s>
<s>
During	O
the	O
match	O
,	O
AlphaZero	B-Application
ran	O
on	O
a	O
single	O
machine	O
with	O
four	O
application-specific	O
TPUs	O
.	O
</s>
<s>
In	O
100	O
games	O
from	O
the	O
normal	O
starting	O
position	O
,	O
AlphaZero	B-Application
won	O
25	O
games	O
as	O
White	O
,	O
won	O
3	O
as	O
Black	O
,	O
and	O
drew	O
the	O
remaining	O
72	O
.	O
</s>
<s>
In	O
a	O
series	O
of	O
twelve	O
,	O
100-game	O
matches	O
(	O
of	O
unspecified	O
time	O
or	O
resource	O
constraints	O
)	O
against	O
Stockfish	B-Application
starting	O
from	O
the	O
12	O
most	O
popular	O
human	O
openings	O
,	O
AlphaZero	B-Application
won	O
290	O
,	O
drew	O
886	O
and	O
lost	O
24	O
.	O
</s>
<s>
AlphaZero	B-Application
was	O
trained	O
on	O
shogi	O
for	O
a	O
total	O
of	O
two	O
hours	O
before	O
the	O
tournament	O
.	O
</s>
<s>
In	O
100	O
shogi	O
games	O
against	O
Elmo	B-Application
(	O
World	O
Computer	O
Shogi	O
Championship	O
27	O
summer	O
2017	O
tournament	O
version	O
with	O
YaneuraOu	O
4.73	O
search	O
)	O
,	O
AlphaZero	B-Application
won	O
90	O
times	O
,	O
lost	O
8	O
times	O
and	O
drew	O
twice	O
.	O
</s>
<s>
As	O
in	O
the	O
chess	B-Application
games	O
,	O
each	O
program	O
got	O
one	O
minute	O
per	O
move	O
,	O
and	O
Elmo	B-Application
was	O
given	O
64	O
threads	O
and	O
a	O
hash	B-Algorithm
size	O
of	O
1GB	O
.	O
</s>
<s>
After	O
34	O
hours	O
of	O
self-learning	O
of	O
Go	O
and	O
against	O
AlphaGo	B-Application
Zero	I-Application
,	O
AlphaZero	B-Application
won	O
60	O
games	O
and	O
lost	O
40	O
.	O
</s>
<s>
DeepMind	B-Application
stated	O
in	O
its	O
preprint	O
,	O
"	O
The	O
game	O
of	O
chess	B-Application
represented	O
the	O
pinnacle	O
of	O
AI	B-Application
research	I-Application
over	O
several	O
decades	O
.	O
</s>
<s>
AlphaZero	B-Application
is	O
a	O
generic	O
reinforcement	O
learning	O
algorithm	O
originally	O
devised	O
for	O
the	O
game	O
of	O
go	O
that	O
achieved	O
superior	O
results	O
within	O
a	O
few	O
hours	O
,	O
searching	O
a	O
thousand	O
times	O
fewer	O
positions	O
,	O
given	O
no	O
domain	O
knowledge	O
except	O
the	O
rules.	O
"	O
</s>
<s>
DeepMind	B-Application
's	O
Demis	O
Hassabis	O
,	O
a	O
chess	B-Application
player	O
himself	O
,	O
called	O
AlphaZero	B-Application
's	O
play	O
style	O
"	O
alien	O
"	O
:	O
It	O
sometimes	O
wins	O
by	O
offering	O
counterintuitive	O
sacrifices	O
,	O
like	O
offering	O
up	O
a	O
queen	O
and	O
bishop	O
to	O
exploit	O
a	O
positional	O
advantage	O
.	O
</s>
<s>
"	O
It	O
's	O
like	O
chess	B-Application
from	O
another	O
dimension.	O
"	O
</s>
<s>
Given	O
the	O
difficulty	O
in	O
chess	B-Application
of	O
forcing	O
a	O
win	O
against	O
a	O
strong	O
opponent	O
,	O
the	O
+28	O
–	O
0	O
=	O
72	O
result	O
is	O
a	O
significant	O
margin	O
of	O
victory	O
.	O
</s>
<s>
However	O
,	O
some	O
grandmasters	O
,	O
such	O
as	O
Hikaru	O
Nakamura	O
and	O
Komodo	B-Application
developer	O
Larry	O
Kaufman	O
,	O
downplayed	O
AlphaZero	B-Application
's	O
victory	O
,	O
arguing	O
that	O
the	O
match	O
would	O
have	O
been	O
closer	O
if	O
the	O
programs	O
had	O
access	O
to	O
an	O
opening	O
database	O
(	O
since	O
Stockfish	B-Application
was	O
optimized	O
for	O
that	O
scenario	O
)	O
.	O
</s>
<s>
Romstad	O
additionally	O
pointed	O
out	O
that	O
Stockfish	B-Application
is	O
not	O
optimized	O
for	O
rigidly	O
fixed-time	O
moves	O
and	O
the	O
version	O
used	O
was	O
a	O
year	O
old	O
.	O
</s>
<s>
Similarly	O
,	O
some	O
shogi	O
observers	O
argued	O
that	O
the	O
Elmo	B-Application
hash	B-Algorithm
size	O
was	O
too	O
low	O
,	O
that	O
the	O
resignation	O
settings	O
and	O
the	O
"	O
EnteringKingRule	O
"	O
settings	O
(	O
cf	O
.	O
</s>
<s>
shogi	O
§	O
Entering	O
King	O
)	O
may	O
have	O
been	O
inappropriate	O
,	O
and	O
that	O
Elmo	B-Application
is	O
already	O
obsolete	O
compared	O
with	O
newer	O
programs	O
.	O
</s>
<s>
Papers	O
headlined	O
that	O
the	O
chess	B-Application
training	O
took	O
only	O
four	O
hours	O
:	O
"	O
It	O
was	O
managed	O
in	O
little	O
more	O
than	O
the	O
time	O
between	O
breakfast	O
and	O
lunch.	O
"	O
</s>
<s>
Wired	O
described	O
AlphaZero	B-Application
as	O
"	O
the	O
first	O
multi-skilled	O
AI	B-Application
board-game	O
champ	O
"	O
.	O
</s>
<s>
AI	B-Application
expert	O
Joanna	O
Bryson	O
noted	O
that	O
Google	O
's	O
"	O
knack	O
for	O
good	O
publicity	O
"	O
was	O
putting	O
it	O
in	O
a	O
strong	O
position	O
against	O
challengers	O
.	O
</s>
<s>
It	O
's	O
also	O
very	O
political	O
,	O
as	O
it	O
helps	O
make	O
Google	O
as	O
strong	O
as	O
possible	O
when	O
negotiating	O
with	O
governments	O
and	O
regulators	O
looking	O
at	O
the	O
AI	B-Application
sector.	O
"	O
</s>
<s>
Human	O
chess	B-Application
grandmasters	O
generally	O
expressed	O
excitement	O
about	O
AlphaZero	B-Application
.	O
</s>
<s>
Danish	O
grandmaster	O
Peter	O
Heine	O
Nielsen	O
likened	O
AlphaZero	B-Application
's	O
play	O
to	O
that	O
of	O
a	O
superior	O
alien	O
species	O
.	O
</s>
<s>
Norwegian	O
grandmaster	O
Jon	O
Ludvig	O
Hammer	O
characterized	O
AlphaZero	B-Application
's	O
play	O
as	O
"	O
insane	O
attacking	O
chess	B-Application
"	O
with	O
profound	O
positional	O
understanding	O
.	O
</s>
<s>
Former	O
champion	O
Garry	O
Kasparov	O
said	O
,	O
"	O
It	O
's	O
a	O
remarkable	O
achievement	O
,	O
even	O
if	O
we	O
should	O
have	O
expected	O
it	O
after	O
AlphaGo.	O
"	O
</s>
<s>
Grandmaster	O
Hikaru	O
Nakamura	O
was	O
less	O
impressed	O
,	O
stating	O
:	O
"	O
I	O
do	O
n't	O
necessarily	O
put	O
a	O
lot	O
of	O
credibility	O
in	O
the	O
results	O
simply	O
because	O
my	O
understanding	O
is	O
that	O
AlphaZero	B-Application
is	O
basically	O
using	O
the	O
Google	O
supercomputer	O
and	O
Stockfish	B-Application
does	O
n't	O
run	O
on	O
that	O
hardware	O
;	O
Stockfish	B-Application
was	O
basically	O
running	O
on	O
what	O
would	O
be	O
my	O
laptop	O
.	O
</s>
<s>
If	O
you	O
wanna	O
have	O
a	O
match	O
that	O
's	O
comparable	O
you	O
have	O
to	O
have	O
Stockfish	B-Application
running	O
on	O
a	O
supercomputer	O
as	O
well.	O
"	O
</s>
<s>
Top	O
US	O
correspondence	O
chess	B-Application
player	O
Wolff	O
Morrow	O
was	O
also	O
unimpressed	O
,	O
claiming	O
that	O
AlphaZero	B-Application
would	O
probably	O
not	O
make	O
the	O
semifinals	O
of	O
a	O
fair	O
competition	O
such	O
as	O
TCEC	O
where	O
all	O
engines	O
play	O
on	O
equal	O
hardware	O
.	O
</s>
<s>
Morrow	O
further	O
stated	O
that	O
although	O
he	O
might	O
not	O
be	O
able	O
to	O
beat	O
AlphaZero	B-Application
if	O
AlphaZero	B-Application
played	O
drawish	O
openings	O
such	O
as	O
the	O
Petroff	O
Defence	O
,	O
AlphaZero	B-Application
would	O
not	O
be	O
able	O
to	O
beat	O
him	O
in	O
a	O
correspondence	O
chess	B-Application
game	O
either	O
.	O
</s>
<s>
Motohiro	O
Isozaki	O
,	O
the	O
author	O
of	O
YaneuraOu	O
,	O
noted	O
that	O
although	O
AlphaZero	B-Application
did	O
comprehensively	O
beat	O
Elmo	B-Application
,	O
the	O
rating	O
of	O
AlphaZero	B-Application
in	O
shogi	O
stopped	O
growing	O
at	O
a	O
point	O
which	O
is	O
at	O
most	O
100	O
–	O
200	O
higher	O
than	O
Elmo	B-Application
.	O
</s>
<s>
This	O
gap	O
is	O
not	O
that	O
high	O
,	O
and	O
Elmo	B-Application
and	O
other	O
shogi	O
software	O
should	O
be	O
able	O
to	O
catch	O
up	O
in	O
1	O
–	O
2	O
years	O
.	O
</s>
<s>
DeepMind	B-Application
addressed	O
many	O
of	O
the	O
criticisms	O
in	O
their	O
final	O
version	O
of	O
the	O
paper	O
,	O
published	O
in	O
December	O
2018	O
in	O
Science	O
.	O
</s>
<s>
They	O
further	O
clarified	O
that	O
AlphaZero	B-Application
was	O
not	O
running	O
on	O
a	O
supercomputer	O
;	O
it	O
was	O
trained	O
using	O
5,000	O
tensor	B-Device
processing	I-Device
units	I-Device
(	O
TPUs	O
)	O
,	O
but	O
only	O
ran	O
on	O
four	O
TPUs	O
and	O
a	O
44-core	O
CPU	O
in	O
its	O
matches	O
.	O
</s>
<s>
In	O
the	O
final	O
results	O
,	O
Stockfish	B-Application
version	O
8	O
ran	O
under	O
the	O
same	O
conditions	O
as	O
in	O
the	O
TCEC	O
superfinal	O
:	O
44	O
CPU	O
cores	O
,	O
Syzygy	O
endgame	O
tablebases	O
,	O
and	O
a	O
32GB	O
hash	B-Algorithm
size	O
.	O
</s>
<s>
In	O
a	O
1000-game	O
match	O
,	O
AlphaZero	B-Application
won	O
with	O
a	O
score	O
of	O
155	O
wins	O
,	O
6	O
losses	O
,	O
and	O
839	O
draws	O
.	O
</s>
<s>
DeepMind	B-Application
also	O
played	O
a	O
series	O
of	O
games	O
using	O
the	O
TCEC	O
opening	O
positions	O
;	O
AlphaZero	B-Application
also	O
won	O
convincingly	O
.	O
</s>
<s>
Stockfish	B-Application
needed	O
10-to-1	O
time	O
odds	O
to	O
match	O
AlphaZero	B-Application
.	O
</s>
<s>
Similar	O
to	O
Stockfish	B-Application
,	O
Elmo	B-Application
ran	O
under	O
the	O
same	O
conditions	O
as	O
in	O
the	O
2017	O
CSA	O
championship	O
.	O
</s>
<s>
The	O
version	O
of	O
Elmo	B-Application
used	O
was	O
WCSC27	O
in	O
combination	O
with	O
YaneuraOu	O
2017	O
Early	O
KPPT	O
4.79	O
64AVX2	O
TOURNAMENT	O
.	O
</s>
<s>
Elmo	B-Application
operated	O
on	O
the	O
same	O
hardware	O
as	O
Stockfish	B-Application
:	O
44	O
CPU	O
cores	O
and	O
a	O
32GB	O
hash	B-Algorithm
size	O
.	O
</s>
<s>
AlphaZero	B-Application
won	O
98.2	O
%	O
of	O
games	O
when	O
playing	O
sente	O
(	O
i.e.	O
</s>
<s>
Human	O
grandmasters	O
were	O
generally	O
impressed	O
with	O
AlphaZero	B-Application
's	O
games	O
against	O
Stockfish	B-Application
.	O
</s>
<s>
Former	O
world	O
champion	O
Garry	O
Kasparov	O
said	O
it	O
was	O
a	O
pleasure	O
to	O
watch	O
AlphaZero	B-Application
play	O
,	O
especially	O
since	O
its	O
style	O
was	O
open	O
and	O
dynamic	O
like	O
his	O
own	O
.	O
</s>
<s>
In	O
the	O
computer	B-Application
chess	I-Application
community	O
,	O
Komodo	B-Application
developer	O
Mark	O
Lefler	O
called	O
it	O
a	O
"	O
pretty	O
amazing	O
achievement	O
"	O
,	O
but	O
also	O
pointed	O
out	O
that	O
the	O
data	O
was	O
old	O
,	O
since	O
Stockfish	B-Application
had	O
gained	O
a	O
lot	O
of	O
strength	O
since	O
January	O
2018	O
(	O
when	O
Stockfish	B-Application
8	O
was	O
released	O
)	O
.	O
</s>
<s>
Fellow	O
developer	O
Larry	O
Kaufman	O
said	O
AlphaZero	B-Application
would	O
probably	O
lose	O
a	O
match	O
against	O
the	O
latest	O
version	O
of	O
Stockfish	B-Application
,	O
Stockfish	B-Application
10	O
,	O
under	O
Top	O
Chess	B-Application
Engine	O
Championship	O
(	O
TCEC	O
)	O
conditions	O
.	O
</s>
<s>
Kaufman	O
argued	O
that	O
the	O
only	O
advantage	O
of	O
neural	B-Architecture
network	I-Architecture
–	O
based	O
engines	O
was	O
that	O
they	O
used	O
a	O
GPU	O
,	O
so	O
if	O
there	O
was	O
no	O
regard	O
for	O
power	O
consumption	O
(	O
e.g.	O
</s>
<s>
Based	O
on	O
this	O
,	O
he	O
stated	O
that	O
the	O
strongest	O
engine	O
was	O
likely	O
to	O
be	O
a	O
hybrid	O
with	O
neural	B-Architecture
networks	I-Architecture
and	O
standard	O
alpha	B-Algorithm
–	I-Algorithm
beta	I-Algorithm
search	I-Algorithm
.	O
</s>
<s>
AlphaZero	B-Application
inspired	O
the	O
computer	B-Application
chess	I-Application
community	O
to	O
develop	O
Leela	B-Application
Chess	I-Application
Zero	I-Application
,	O
using	O
the	O
same	O
techniques	O
as	O
AlphaZero	B-Application
.	O
</s>
<s>
Leela	O
contested	O
several	O
championships	O
against	O
Stockfish	B-Application
,	O
where	O
it	O
showed	O
roughly	O
similar	O
strength	O
to	O
Stockfish	B-Application
,	O
although	O
Stockfish	B-Application
has	O
since	O
pulled	O
away	O
.	O
</s>
<s>
In	O
2019	O
DeepMind	B-Application
published	O
MuZero	B-Application
,	O
a	O
unified	O
system	O
that	O
played	O
excellent	O
chess	B-Application
,	O
shogi	O
,	O
and	O
go	O
,	O
as	O
well	O
as	O
games	O
in	O
the	O
Atari	B-General_Concept
Learning	O
Environment	O
,	O
without	O
being	O
pre-programmed	O
with	O
their	O
rules	O
.	O
</s>
