I
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o
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E
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rica
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g
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Co
m
pu
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er
Science
Vo
l.
25
,
No
.
1
,
J
an
u
ar
y
20
22
,
p
p
.
4
8
1
~
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8
7
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n
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K
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w
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s
:
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to
ML
C
o
m
p
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r
a
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s
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s
f
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eu
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k
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t le
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T
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s
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ss
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CC B
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se
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C
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r
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s
p
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A
uth
o
r
:
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a
Ku
m
ar
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ed
d
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Dep
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(
Au
to
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m
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My
lav
ar
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,
A.
P,
I
n
d
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E
-
m
ail: V
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ak
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ar
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8
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co
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1.
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NT
RO
D
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lo
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-
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tan
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in
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m
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d
d
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g
u
p
to
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ate
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les [
1
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,
[
2
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.
Th
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ith
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ize
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f
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ate
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s
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m
ally
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e
p
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ate
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r
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ch
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r
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en
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eu
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ally
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tim
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with
g
r
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b
ased
tech
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iq
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es [
3
]
,
[
4
]
.
T
h
er
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is
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n
l
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s
o
m
e
p
r
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it
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s
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ch
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T
h
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m
o
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s
tr
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co
m
m
u
n
icativ
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en
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g
h
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o
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m
s
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m
s
an
d
also
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ter
p
r
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T
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r
ap
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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J
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p
Sci
,
Vo
l.
25
,
No
.
1
,
J
an
u
ar
y
20
22
:
481
-
4
8
7
482
illu
s
tr
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ca
n
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an
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lear
n
i
n
g
R
ein
f
o
r
ce
m
en
t
lear
n
in
g
is
p
a
r
t
o
f
lear
n
in
g
tech
n
i
q
u
e
i
n
m
ac
h
in
e
lear
n
in
g
.
T
h
ey
ar
e
s
u
p
er
v
is
ed
,
u
n
s
u
p
er
v
is
ed
an
d
r
ein
f
o
r
ce
m
en
t
lear
n
in
g
’
s
[
7
]
,
[
8
]
.
W
e
d
is
cu
s
s
a
r
ein
f
o
r
ce
m
en
t
lear
n
in
g
alg
o
r
ith
m
f
o
r
an
au
to
m
atic
p
r
e
d
ictio
n
.
T
h
e
p
ap
er
is
p
r
esen
ted
in
th
e
f
o
llo
win
g
m
an
n
e
r
:
t
h
e
n
e
x
t
s
ec
tio
n
d
is
cu
s
s
th
e
b
ac
k
g
r
o
u
n
d
an
al
y
s
is
.
Sectio
n
3
d
escr
ib
es
r
ein
f
o
r
ce
m
en
t
lear
n
in
g
alg
o
r
ith
m
m
u
tatio
n
g
r
a
p
h
.
An
en
v
ir
o
n
m
en
tal
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
d
escr
ib
es
in
s
ec
tio
n
4
.
Sectio
n
5
d
escr
i
b
es
en
v
ir
o
n
m
en
tal
lear
n
in
g
alg
o
r
ith
m
s
an
d
co
n
cl
u
s
io
n
in
s
ec
tio
n
6
.
2.
T
H
E
P
RO
P
O
SE
D
M
E
T
H
O
D
AND
B
ACK
G
RO
UN
D
A
NALYS
I
S
I
n
d
ee
p
n
e
u
r
al
n
etwo
r
k
,
m
u
lti
-
ag
en
t
ty
p
es
o
f
en
v
ir
o
n
m
e
n
ts
ar
e
ex
tr
em
ely
d
y
n
am
ic,
th
ey
i
m
p
ac
t
o
n
n
eig
h
b
o
r
s
f
o
r
alter
s
r
ap
id
ly
.
T
h
is
o
p
er
atio
n
is
to
u
g
h
to
le
ar
n
th
e
in
ter
p
r
etatio
n
b
etwe
en
th
e
elem
en
ts
.
T
h
e
co
n
v
o
l
u
tio
n
al
r
ein
f
o
r
ce
m
en
t
l
ea
r
n
in
g
g
r
a
p
h
ac
co
m
m
o
d
ates
th
e
d
y
n
am
ic
s
o
f
th
e
g
r
ap
h
o
f
t
h
e
n
u
m
er
o
u
s
ag
en
t
en
v
ir
o
n
m
en
ts
,
an
d
t
h
is
d
y
n
a
m
ic
k
n
o
wled
g
e
im
p
r
is
o
n
s
th
e
r
elativ
e
b
etwe
en
ag
e
n
ts
b
y
t
h
eir
r
ep
r
esen
tatio
n
.
Do
r
m
an
t
f
ea
tu
r
es
g
en
er
ated
b
y
co
n
v
o
lu
tio
n
al
lay
er
s
f
r
o
m
a
cc
ess
ib
le
f
ield
s
ar
e
o
p
p
r
ess
ed
to
lear
n
team
wo
r
k
;
f
in
ally
d
escr
ib
e
th
e
p
r
o
p
o
s
ed
m
eth
o
d
s
u
b
s
tan
tially
p
er
f
o
r
m
s
ex
is
tin
g
tech
n
iq
u
es
in
a
d
iv
er
s
ity
o
f
co
o
p
er
ativ
e
s
ce
n
ar
io
s
[
9
]
,
[
10]
.
I
n
r
ec
e
n
t
y
ea
r
s
,
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
s
h
as
g
ain
ed
r
is
in
g
atten
tio
n
a
n
d
ef
f
o
r
ts
to
g
et
b
etter
it h
av
e
g
r
o
w
n
-
u
p
s
ig
n
if
i
ca
n
t
ly
.
A
s
et
o
f
m
ea
s
u
r
em
e
n
ts
th
at
q
u
an
titativ
ely
co
m
p
u
te
d
i
s
s
im
ilar
asp
ec
ts
o
f
r
eliab
ilit
y
an
d
we
s
p
o
tlig
h
t
o
n
v
ar
iety
an
d
r
is
k
f
ac
to
r
d
u
r
i
n
g
tr
ain
in
g
an
d
af
ter
lear
n
in
g
.
T
h
ese
m
etr
ics
ar
e
d
esig
n
ed
to
b
e
g
en
er
al
p
u
r
p
o
s
e
with
s
tatis
tica
l
test
s
to
allo
w
m
eticu
l
o
u
s
co
m
p
ar
is
o
n
s
o
n
th
ese
m
etr
ics.
W
e
ap
p
ly
o
u
r
m
etr
ics
to
a
s
et
o
f
co
m
m
o
n
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
s
an
d
th
ei
r
en
v
ir
o
n
m
en
ts
f
o
r
co
m
p
ar
is
o
n
a
n
d
a
n
aly
ze
th
e
o
u
tp
u
t
[
1
1
]
.
Gen
er
ally
,
r
ei
n
f
o
r
ce
m
e
n
t
lear
n
in
g
ag
e
n
ts
with
two
cr
u
cial
o
b
jectiv
es.
Prim
ar
y
o
n
e
is
to
b
r
in
g
to
g
eth
er
o
b
v
io
u
s
,
r
ev
ea
l
in
g
an
d
s
ca
lab
le
is
s
u
es
th
at
im
p
r
is
o
n
k
ey
p
r
o
b
lem
in
ten
d
o
f
g
e
n
er
al
an
d
well
-
o
r
g
an
ized
lear
n
i
n
g
alg
o
r
ith
m
s
.
T
h
e
s
ec
o
n
d
o
b
jectiv
e
to
lea
r
n
ag
en
t
b
eh
a
v
io
u
r
th
r
o
u
g
h
th
eir
t
h
r
o
u
g
h
p
u
t o
n
th
ese
co
m
m
u
n
al
b
e
n
ch
m
a
r
k
s
[
1
2
]
,
[
1
3
]
.
I
n
d
ee
p
r
ein
f
o
r
ce
m
en
t
lea
r
n
i
n
g
alg
o
r
ith
m
s
h
an
d
le
with
r
o
b
u
s
t
v
alu
e
f
u
n
ctio
n
s
f
o
r
u
n
p
r
o
ce
s
s
ed
clar
if
icatio
n
an
d
r
ewa
r
d
s
f
o
r
m
o
d
el
-
f
r
ee
a
n
d
m
o
d
el
-
b
ased
lear
n
in
g
alg
o
r
ith
m
s
.
I
n
th
ese
alg
o
r
ith
m
s
,
s
u
cc
ess
o
r
r
ep
r
esen
tatio
n
s
ar
e
d
ec
o
m
p
o
s
es
th
e
v
alu
e
f
u
n
ctio
n
in
t
o
2
m
ec
h
an
is
m
s
;
th
ese
m
ec
h
an
is
m
s
ar
e
r
ewa
r
d
p
r
ed
icto
r
a
n
d
s
u
cc
ess
o
r
m
ap
.
T
h
e
r
ewa
r
d
p
r
ed
icto
r
m
ap
s
d
escr
ib
e
to
s
ca
lar
r
ewa
r
d
s
an
d
th
e
s
u
cc
ess
o
r
m
ap
p
r
esen
ts
th
e
p
r
ed
ictab
le
f
u
tu
r
e
s
itu
atio
n
ten
u
r
e
f
r
o
m
an
y
g
iv
en
co
n
d
itio
n
.
I
n
t
h
is
co
n
ce
p
t,
th
e
v
alu
e
f
u
n
cti
o
n
o
f
a
c
o
n
d
itio
n
ca
n
b
e
ca
lc
u
lated
as
th
e
in
n
er
p
r
o
d
u
ct
b
etwe
en
th
e
m
a
p
a
n
d
th
e
weig
h
ts
o
f
r
ewa
r
d
p
o
i
n
ts
.
Mo
s
t
o
f
th
ese
ty
p
es
o
f
alg
o
r
ith
m
s
u
s
ed
d
ee
p
s
u
cc
ess
o
r
r
ein
f
o
r
c
em
en
t
lear
n
in
g
(
DSR
)
th
ey
g
en
er
alize
s
u
cc
ess
o
r
r
ep
r
esen
tatio
n
s
(
SR
)
with
in
a
b
ac
k
-
to
-
ba
ck
d
ee
p
r
ein
f
o
r
ce
m
en
t le
ar
n
in
g
f
r
am
ewo
r
k
[
1
4
]
,
[
15]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Th
e
g
en
era
l d
esig
n
o
f th
e
a
u
to
ma
tio
n
fo
r
mu
ltip
le
field
s
u
s
in
g
…
(
V
ija
ya
K
u
ma
r
R
ed
d
y
R
a
d
h
a
)
483
2
.
1
.
Reinf
o
rc
e
m
ent
a
lg
o
rit
hm
a
s
im
pu
t
a
t
i
o
n g
ra
ph
T
h
e
m
em
o
r
y
an
d
co
m
p
u
tatio
n
r
eq
u
ir
e
d
f
o
r
th
e
Q
-
v
alu
e
alg
o
r
ith
m
wo
u
ld
b
e
to
o
h
ig
h
.
T
h
u
s
,
a
d
ee
p
n
etwo
r
k
Q
-
L
ea
r
n
i
n
g
f
u
n
ctio
n
ap
p
r
o
x
im
ato
r
is
u
s
ed
in
s
tead
.
T
h
is
lear
n
in
g
alg
o
r
ith
m
is
ca
lled
d
ee
p
Q
-
n
etwo
r
k
(
DQN)
.
T
h
e
k
ey
i
d
ea
in
th
is
d
ev
elo
p
m
e
n
t
was
th
u
s
to
u
s
e
d
ee
p
n
e
u
r
al
n
etwo
r
k
s
to
r
ep
r
e
s
en
t
th
e
Q
-
n
etwo
r
k
an
d
tr
ain
th
is
n
etwo
r
k
to
p
r
ed
ict
to
tal
r
ewa
r
d
.
DQN
is
Q
-
lear
n
in
g
o
f
n
e
u
r
al
n
etwo
r
k
s
,
th
e
m
o
tiv
atio
n
at
th
e
b
ac
k
is
m
er
ely
co
n
n
ec
ted
to
b
ig
s
tate
s
p
ac
e
en
v
ir
o
n
m
en
ts
wh
er
e
v
ital
a
Q
-
tab
le
wo
u
ld
b
e
a
tr
em
en
d
o
u
s
ly
co
m
p
lex
,
d
if
f
icu
lt
an
d
p
r
o
tr
ac
ted
task
.
As
an
alter
n
ativ
e
o
f
a
Q
-
tab
le
n
eu
r
al
n
etwo
r
k
s
esti
m
ated
Q
-
v
alu
es
f
o
r
ea
ch
ex
p
lo
it
b
ased
o
n
t
h
e
co
n
d
itio
n
.
Gr
ap
h
s
r
ep
r
esen
tin
g
n
eu
r
al
n
etwo
r
k
ar
ch
itectu
r
es
in
s
p
ir
ed
b
y
o
v
er
th
e
s
p
ac
e,
in
r
ei
n
f
o
r
ce
m
e
n
t
lear
n
in
g
al
g
o
r
ith
m
s
b
y
o
n
b
eh
alf
o
f
th
e
lo
s
s
f
u
n
ctio
n
o
f
a
r
e
in
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
as
ac
cu
s
atio
n
as
a
d
ir
ec
ted
ac
y
clic
g
r
ap
h
f
o
r
t
h
e
lo
s
s
f
u
n
ctio
n
,
with
n
o
d
es
o
n
b
eh
al
f
o
f
in
p
u
ts
,
o
p
e
r
ato
r
s
,
p
ar
am
eter
s
an
d
o
u
tco
m
e.
Fo
r
e
x
am
p
le,
i
n
th
e
p
r
o
ce
s
s
in
g
g
r
a
p
h
f
o
r
DQN
,
in
p
u
t
n
o
d
es
co
n
tain
d
ata
f
r
o
m
th
e
r
ep
ea
t
b
ar
r
ier
,
o
p
er
ativ
e
n
o
d
es
co
m
p
r
is
e
n
eu
r
al
n
etwo
r
k
o
p
er
ato
r
s
an
d
f
u
n
d
am
en
tal
m
ath
o
p
er
ato
r
s
,
an
d
th
e
o
u
tco
m
e
n
o
d
e
r
ep
r
esen
t
th
e
lo
s
s
,
wh
ich
will
b
e
m
in
im
ize
with
g
r
ad
ie
n
t
d
escen
t.
Fig
u
r
e
2
s
h
o
w
h
o
w
th
e
s
q
u
ar
ed
B
ellm
an
E
r
r
o
r
will b
e
u
s
ed
to
g
et
t
h
r
r
e
q
u
ir
ed
o
u
tp
u
t.
Fig
u
r
e
2
.
E
x
am
p
l
e
o
f
s
q
u
ar
e
d
B
ellm
an
er
r
o
r
(
1
6
)
W
e
c
a
n
r
e
c
o
g
n
i
z
e
,
w
h
y
a
l
e
a
r
n
e
d
a
l
g
o
r
i
t
h
m
i
s
e
n
h
a
n
c
e
d
,
a
n
d
t
h
e
n
t
h
e
y
c
a
n
t
o
g
e
t
h
e
r
a
d
j
u
s
t
t
h
e
d
o
m
e
s
t
i
c
m
e
c
h
a
n
i
s
m
o
f
t
h
e
a
l
g
o
r
i
t
h
m
t
o
a
d
v
a
n
c
e
i
t
a
n
d
t
r
a
n
s
f
e
r
t
h
e
h
e
l
p
f
u
l
m
e
c
h
a
n
i
s
m
t
o
a
d
d
i
t
i
o
n
a
l
i
s
s
u
e
s
.
F
i
n
a
l
l
y
,
t
h
e
i
l
l
u
s
t
r
a
t
i
o
n
s
u
p
p
o
r
t
s
g
e
n
e
r
a
l
a
l
g
o
r
i
t
h
m
s
t
h
a
t
c
a
n
r
e
s
o
l
v
e
an
e
x
t
e
n
s
i
v
e
v
a
r
i
e
t
y
o
f
i
s
s
u
e
s
i
n
F
i
g
u
r
e
2
[
1
6
]
.
W
e
d
ev
elo
p
e
d
th
is
r
ep
r
esen
tatio
n
u
s
in
g
th
e
p
y
th
o
n
Py
Glo
v
e
li
b
r
ar
y
,
wh
ich
a
p
p
r
o
p
r
iately
t
u
r
n
s
th
e
ex
ce
e
d
in
g
g
r
ap
h
i
n
to
a
in
v
esti
g
ate
s
p
ac
e
th
at
ca
n
b
e
o
p
tim
ized
with
s
ta
n
d
ar
d
ize
d
ev
elo
p
m
en
t in
to
(
1
)
.
L
D
Q
N
= (
Q
ε
(
S
t
,
a
t
)
–
(
r
t
+
γ
*
ma
x
a
Q
ε
′
(
S
t
+
1
,
a
))
(
1
)
Mo
d
el
-
b
ased
r
ein
f
o
r
ce
m
en
t
lear
n
in
g
h
as
a
ac
tu
ally
in
f
lu
en
ti
al
f
r
o
m
co
n
tr
o
l
t
h
eo
r
y
,
an
d
th
e
in
ten
tio
n
is
to
g
r
ap
h
t
h
r
o
u
g
h
a
n
f
(
s
,
a)
co
n
tr
o
l
f
u
n
ctio
n
to
ch
o
o
s
e
th
e
m
o
s
t
ex
ce
llen
t
p
r
o
b
ab
le
ac
ti
o
n
s
.
I
t
is
s
im
ilar
as
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
f
ield
s
wh
er
e
th
e
laws
o
f
p
h
y
s
ics
ar
e
co
n
tr
ib
u
te
d
b
y
t
h
e
o
r
ig
i
n
ato
r
.
T
h
e
d
if
f
icu
lty
o
f
m
o
d
el
-
b
ased
m
et
h
o
d
s
is
th
at
alth
o
u
g
h
t
h
ey
h
a
v
e
ex
tr
a
s
u
p
p
o
s
itio
n
an
d
esti
m
ate
o
n
a
p
a
r
t
icu
lar
jo
b
,
b
u
t
m
ay
b
e
in
co
m
p
lete
o
n
ly
to
th
ese
co
r
r
ec
t
ty
p
es
o
f
task
s
.
T
h
e
r
e
ar
e
two
m
ain
ap
p
r
o
ac
h
es:
lea
r
n
in
g
th
e
m
o
d
el
o
r
lear
n
g
iv
en
th
e
d
esig
n
.
2
.
2
.
E
nv
iro
nm
ent
o
f
re
info
r
ce
m
ent
lea
rning
W
e
u
tili
ze
an
ev
o
l
u
tio
n
ar
y
b
ased
p
r
o
ce
d
u
r
e
to
o
p
tim
ize
t
h
e
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
s
o
f
atten
tio
n
[
1
7
]
,
[
1
8
]
.
First,
we
in
itialize
a
p
o
p
u
lace
o
f
tr
ain
in
g
ag
en
ts
with
r
an
d
o
m
ized
g
r
a
p
h
s
.
T
h
is
p
o
p
u
lac
e
o
f
ag
e
n
ts
is
tr
ain
ed
in
eq
u
iv
al
en
t
o
v
e
r
a
s
et
o
f
tr
ain
in
g
en
v
i
r
o
n
m
en
ts
.
T
h
e
ag
en
t’
s
f
ir
s
t
tr
ain
o
n
a
d
if
f
icu
lty
en
v
ir
o
n
m
en
t
p
r
o
jecte
d
to
r
a
p
id
ly
o
u
t
with
p
o
o
r
p
er
f
o
r
m
in
g
is
s
u
es.
I
f
an
ag
en
t
ca
n
’
t
c
r
ac
k
th
e
d
if
f
icu
lty
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2502
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
,
Vo
l.
25
,
No
.
1
,
J
an
u
ar
y
20
22
:
481
-
4
8
7
484
en
v
ir
o
n
m
en
t,
th
e
tr
ain
in
g
is
s
to
p
p
ed
u
p
n
ea
r
th
e
b
eg
in
n
in
g
with
a
s
co
r
e
o
f
ze
r
o
.
Oth
e
r
wis
e,
th
e
tr
ain
in
g
p
r
o
ce
ed
s
to
m
o
r
e
h
ar
d
en
v
ir
o
n
m
en
ts
.
T
h
e
alg
o
r
ith
m
th
r
o
u
g
h
p
u
t
is
ev
alu
ated
an
d
u
s
ed
to
b
r
in
g
u
p
to
d
ate
th
e
p
o
p
u
lace
,
wh
er
e
m
o
r
e
talen
te
d
alg
o
r
ith
m
s
ar
e
f
u
r
th
er
m
u
ta
ted
.
T
o
d
ec
r
ea
s
e
th
e
s
ea
r
c
h
s
p
ac
e,
th
e
n
we
u
s
e
a
f
u
n
ctio
n
al
co
r
r
esp
o
n
d
e
n
ce
m
a
n
ag
er
w
h
ich
will
b
o
u
n
ce
o
v
e
r
r
ec
en
tly
p
r
o
jecte
d
alg
o
r
ith
m
s
.
T
h
ese
alg
o
r
ith
m
s
ar
e
s
am
e
as
p
r
ev
i
o
u
s
ly
p
r
ac
tical
ex
am
in
ed
alg
o
r
ith
m
s
.
T
h
is
lo
o
p
co
n
tin
u
es
as
n
o
v
el
m
u
tate
ag
en
t
alg
o
r
ith
m
s
ar
e
tr
ain
ed
a
n
d
e
v
alu
ate.
At
t
h
e
en
d
in
g
o
f
tr
ain
in
g
,
we
c
h
o
o
s
e
th
e
m
o
s
t
ex
ce
llen
t
alg
o
r
it
h
m
an
d
ap
p
r
aise
its
th
r
o
u
g
h
p
u
t
o
v
er
a
s
et
o
f
h
id
d
en
test
en
v
ir
o
n
m
en
ts
.
Fig
u
r
e
3
s
h
o
w
h
o
w
th
e
t
h
e
m
eta
-
lear
n
in
g
m
et
o
d
will
b
e
u
s
ed
f
o
r
tr
ai
n
in
g
a
n
d
test
in
g
it
f
o
r
m
u
ltip
le
ti
m
es.
Fig
u
r
e
3
.
Ov
e
r
v
iew
o
f
m
eta
-
le
ar
n
in
g
m
et
h
o
d
3.
M
E
T
H
O
DO
L
O
G
Y
AND
R
E
SU
L
T
S
W
e
ex
p
o
s
e
two
f
in
d
in
g
alg
o
r
ith
m
s
th
at
s
h
o
w
h
ig
h
-
q
u
ality
g
en
er
aliza
tio
n
th
r
o
u
g
h
p
u
t.
T
h
e
p
r
im
ar
y
d
ee
p
alg
o
r
ith
m
is
DQNReg
,
wh
ich
b
u
ild
o
n
DQN
b
y
ad
d
itio
n
h
ea
v
i
n
ess
o
n
th
e
Q
-
v
alu
e
s
b
ased
o
n
s
tan
d
ar
d
s
q
u
ar
ed
B
ellm
an
er
r
o
r
[
1
9
]
.
T
h
e
n
ex
t
lear
n
ed
lo
s
s
f
u
n
ctio
n
,
DQNCli
p
p
ed
,
is
ad
d
itio
n
al
m
u
ltifa
ce
ted
,
an
d
it’s
d
o
m
in
ate
ter
m
h
as
a
s
tr
aig
h
tf
o
r
war
d
f
o
r
m
-
t
h
e
m
ax
im
u
m
o
f
th
e
Q
-
v
alu
e
a
n
d
th
e
s
q
u
ar
ed
B
ellm
an
er
r
o
r
th
at
m
ea
n
s
m
o
d
u
lo
a
co
n
s
tan
t.
T
wo
alg
o
r
ith
m
s
ca
n
b
e
v
iew
as
a
m
an
n
er
to
n
o
r
m
alize
th
e
Q
-
v
alu
es.
W
h
ile
DQNReg
ad
d
a
s
o
f
t
co
n
s
tr
ictio
n
,
DQNCli
p
p
ed
ca
n
b
e
in
ter
p
r
etin
g
as
a
ty
p
e
o
f
c
o
n
s
tr
ain
e
d
o
p
tim
izat
io
n
th
at
will
r
ed
u
ce
t
h
e
Q
-
v
alu
es,
if
t
h
ey
b
ec
o
m
e
to
o
h
ef
t
y
.
W
e
d
em
o
n
s
tr
ate
th
at
th
is
lear
n
ed
c
o
n
s
tr
ictio
n
k
ic
k
s
in
d
u
r
in
g
th
e
n
ea
r
th
e
b
e
g
in
n
in
g
p
h
ase
o
f
tr
ain
in
g
wh
en
o
v
er
es
tim
ate
th
e
Q
-
v
alu
es
is
a
p
o
ten
tial
p
r
o
b
lem
.
On
ce
th
is
co
n
s
tr
ain
t is p
leased
,
th
en
th
e
lo
s
s
will m
in
im
ize
in
s
tead
o
f
th
e
o
r
ig
in
al
s
q
u
a
r
ed
B
ellm
an
er
r
o
r
[
2
0
]
,
[
2
1
]
.
T
h
e
f
o
llo
win
g
alg
o
r
ith
m
DQ
NR
eg
f
o
r
r
ein
f
o
r
ce
m
en
t
lear
n
in
g
in
b
etter
way
to
an
aly
ze
t
h
e
ac
cu
r
ate
p
r
ed
ictio
n
s
.
Alo
n
g
with
th
is
alg
o
r
ith
m
,
o
th
er
alg
o
r
ith
m
s
ar
e
wo
r
k
in
g
f
o
r
b
ette
r
lea
r
n
in
g
f
o
r
ac
cu
r
ate
esti
m
atio
n
o
f
v
alu
es.
T
h
ese
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
alg
o
r
ith
m
s
ev
er
y
s
tep
u
p
d
ates
th
e
d
ata
u
s
in
g
b
u
f
f
er
s
p
ac
e.
C
h
ec
k
th
e
s
am
p
les f
o
r
co
m
p
u
t
e
th
e
tar
g
et
v
alu
es,
f
o
r
th
is
we
p
er
f
o
r
m
th
e
g
r
ad
ien
t d
escen
t step
an
d
u
p
d
ate
th
e
tar
g
et
n
etwo
r
k
p
ar
a
m
eter
s
.
T
h
is
lear
n
in
g
co
n
s
is
ts
o
f
m
u
ltip
le
co
n
ce
p
ts
f
o
r
ac
cu
r
ate
lear
n
in
g
f
o
r
g
en
er
atin
g
th
e
ac
cu
r
ate
r
esu
lts
f
o
r
en
d
u
s
er
s
.
T
h
e
f
o
llo
win
g
alg
o
r
ith
m
g
iv
en
r
ein
f
o
r
ce
m
en
t le
a
r
n
in
g
o
f
DQNReg
.
Alg
o
r
ith
m
f
o
r
DQNReg
Step 1: Initialize the networks with b
uffer
Step 2: for each iteration do
Step 3: for each environment step do
Step 4: Observe the state of the element and then select
Step 5: Execute that state and move to next state
Step 6: Store the information in buffer
Step 7: for each update step do
Step 8: Check the samples
Step 9: Compute the target Value
Step 10: Perform Gradient descent step
Step 11: Update the target network parameters
Step 12: end
A
q
u
ick
er
an
aly
s
is
s
h
o
ws
th
at
wh
ile
f
u
n
d
am
en
tallin
es
lik
e
DQN
f
r
eq
u
en
tly
o
v
er
esti
m
ate
R
-
v
alu
es,
o
u
r
lear
n
e
d
alg
o
r
ith
m
s
d
ea
l
with
th
is
p
r
o
b
lem
in
d
is
s
im
ilar
m
eth
o
d
s
[
2
2
]
.
DQNReg
u
n
d
er
esti
m
ate
th
e
R
-
v
alu
es,
wh
ile
DQN
C
lip
p
ed
h
as
alik
e
p
er
f
o
r
m
an
ce
to
d
o
u
b
l
e
DQN
in
th
at
it
g
r
ad
u
ally
s
l
o
ws
p
r
o
ce
d
u
r
es
th
e
g
r
o
u
n
d
r
ea
lity
with
o
u
t
o
v
er
est
im
atin
g
it.
W
e
d
em
e
n
cy
a
d
at
aset
o
f
to
p
2
0
0
0
p
er
f
o
r
m
in
g
a
lg
o
r
ith
m
s
ex
p
o
s
ed
d
u
r
in
g
p
r
o
g
r
ess
.
I
n
q
u
is
itiv
e
r
ea
d
er
co
u
ld
f
u
r
th
er
e
x
am
in
e
t
h
e
p
r
o
p
e
r
ty
o
f
th
ese
lear
n
e
d
lo
s
s
f
u
n
ctio
n
s
.
Ou
r
tech
n
iq
u
e
lear
n
s
alg
o
r
ith
m
s
th
at
h
av
e
estab
lis
h
a
way
to
r
eg
u
lar
ize
th
e
Q
-
v
alu
es
an
d
th
u
s
d
ec
r
ea
s
e
o
v
er
esti
m
atio
n
[
2
3
]
,
[
2
4
]
.
Fi
g
u
r
e
4
is
u
s
ed
to
s
h
o
w
t
h
e
r
esu
lts
o
f
m
in
i
g
r
id
-
d
o
o
r
k
e
y
f
o
r
v
alu
e
b
ased
R
L
m
eth
o
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
Th
e
g
en
era
l d
esig
n
o
f th
e
a
u
to
ma
tio
n
fo
r
mu
ltip
le
field
s
u
s
in
g
…
(
V
ija
ya
K
u
ma
r
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c
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v
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jay
a
k
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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d
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p
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:
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6
3
9
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),
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tern
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iet
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it
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c
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tac
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lak
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ip
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t
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m
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c
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v
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to
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,
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d
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Re
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s
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g
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a
c
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tam
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g
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t
Be
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p
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tern
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e
ICRTC
-
20
2
1
.
Two
p
a
ten
s
a
re
p
u
b
li
sh
e
d
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
trav
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u
m
a
r@k
l
u
n
i
v
e
rsity
.
i
n
.
Pa
r
u
c
h
u
r
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Ra
v
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k
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sh
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sista
n
t
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ro
fe
ss
o
r
De
p
a
rtem
tn
o
f
In
fo
rm
a
ti
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t
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sa
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t
lu
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id
d
h
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rth
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In
stit
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te
o
f
Tec
h
n
o
lo
g
y
,
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n
u
r
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Vija
y
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wa
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a
.
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h
o
l
d
s
a
M
.
Tec
h
De
g
re
e
fr
o
m
A
c
h
a
ry
a
Na
g
a
rju
n
a
Un
i
v
e
rsity
.
His
re
a
se
ra
c
h
a
re
a
s
a
re
Da
ta
An
a
ly
ti
c
s,
Blo
c
k
c
h
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in
Tec
h
n
o
lo
g
ies
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
r
a
v
ip
ra
k
a
sh
p
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ru
c
h
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ri@p
v
p
si
d
d
h
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rth
a
.
a
c
.
in
a
n
d
p
rp
p
v
p
sit@g
m
a
il
.
c
o
m
.
Evaluation Warning : The document was created with Spire.PDF for Python.