5. Intelligent Cooperative Systems Lab. The University of TokyoICS
オンラインセンサー選択問題
• ラウンドtごとにセンサー を選択すると，
効果 が得られる
5
様々な組み合わせで
試す必要あり
選択されたセンサーの
効能がわかる
2
3
2
6. Intelligent Cooperative Systems Lab. The University of TokyoICS
オンライン貪欲選択アルゴリズム
• ラウンドtごとに，組み合わせ を選択
6
定理 [Streeter
&
Golovin
‘08]:
Online
Greedy
(OG)
オンライン貪欲選択アルゴリズムの性能は，
オフラインでの性能に収束する
Value
of
単一センサーの
選択アルゴリズム
7. Intelligent Cooperative Systems Lab. The University of TokyoICS
7
定理 [Auer
et
al
‘95]:
EXP3で得られる効能の平均は，最適値に収束する
学習と利益追求の
トレードオフパラメータ
単⼀一センサーの選択アルゴリズム
センサーを⼀一つ選択して，その価値を測定
センサー数Nに比例した
計算とメモリが必要
センサーの
選ばれやすさ
サンプリング
EXP3
[Auer
et
al
‘95]
（強化学習の一種）
センサーの重みを学習
8. Intelligent Cooperative Systems Lab. The University of TokyoICS
分散サンプリング
集中的なサンプリングの計算ではスケールしないことも
キーアイディア：センサごとに独⽴立立にサンプリング
8
P(1)
P(2)
P(3)
9. Intelligent Cooperative Systems Lab. The University of TokyoICS
分散サンプリングの⽅方法
• 少ないメッセージのやり取りで可能
9
定理:
この計算でEXP3と同じ確率でサンプリングされる．
4回以下のブロードキャスト通信のみで可能．
P(1)
P(2)
P(3)
15. Intelligent Cooperative Systems Lab. The University of TokyoICS
劣劣モジュラ関係についてもっと勉強したい⼈人
• Tutorialなど
– Andreas Krauseら http://submodularity.org/
15
16. Online
Distributed
Sensor
SelecRon
Daniel
Golovin,
MaUhew
Faulkner,
Andreas
Krause
rsrg @caltech
..where theory and practice collide16
17. Sensor-‐equipped
cell
phones
are
ubiquitous.
Which
sensors
should
send
data?
Can
current
measurements
inform
selecHon?
17
Community
Sensing
Used
for
traffic
monitoring,
polluRon
detecRon,
earthquake
measurement.
Constraints
on
bandwidth,
power,
privacy…
ImpracRcal
to
query
all
phones.
18. 4
Select
two
cameras
to
query,
in
order
to
detect
the
most
people.
18
A
Sensor
SelecRon
Problem
People
Detected:
2
Duplicates
only
counted
once
19. Set
V
of
sensors,
|V|
=
N
Select
a
set
of
k
sensors
Sensing
quality
model
Typically
NP-‐hard…
A
Sensor
SelecRon
Problem
19
20. 20
Submodularity
Diminishing
returns
property
for
adding
more
sensors.
Many
objec0ves
are
submodular:
DetecRon,
coverage,
mutual
informaRon,
and
others.
+2
+1
For
all
,
and
a
sensor
,
21. Lets
choose
sensors
S
=
{v1
,
…
,
vk}
greedily
[Nemhauser
et
al
‘78]
If
F
is
submodular,
the
Greedy
algorithm
gives
constant
factor
approximaRon:
Greedy
SelecRon
1. Must
know
sensing
model
F
2. Greedy
is
centralized
3. SelecHon
ignores
current
sensor
values
21
22. 22
Online
Sensor
SelecRon
Get
to
choose
sensors
on
each
round
t.
Then
is
revealed.
Need
to
explore
different
sets.
Only
need
to
evaluate
F
for
chosen
sets.
2
3
2
23. 23
Online
Sensor
SelecRon
Get
to
choose
sensors
on
each
round
t.
Then
is
revealed.
Round
1
Round
2
Round
3
Only
assume
is
submodular
and
bounded
24. 24
Online
Greedy
SelecRon
At
each
round,
choose
a
set
.
Learn
to
choose
greedily.
Theorem
[Streeter
&
Golovin
‘08]:
Online
Greedy
(OG)
The
centralized
Online
Greedy
algorithm
chooses
Value
of
What
algorithm?
25. 25
On
each
round,
choose
one
sensor
and
observe
it
value.
Theorem
[Auer
et
al
‘95]:
The
average
value
obtained
by
EXP3
converges
to
the
value
of
the
fixed
opRmum:
Single
Sensor
SelecRon
EXP3
[Auer
et
al
‘95]
balances
exploring
and
exploiRng
Can
we
avoid
centralized
sampling?
26. 26
Idea:
Independent
draws
unRl
exactly
one
sensor
broadcasts
a
success.
Distributed
Sampling
Doesn’t
sample
from
correct
distribuHon
P(1)
P(2)
P(3)
Centralized
sampling
may
not
scale
pracRcally.
27. 27
A
Distributed
Sampling
Protocol
Theorem:
Protocol
correctly
samples
from
P.
Requires
<
4
messages
in
the
broadcast
model
We
can
sample
from
correct
distribuRon,
while
using
few
messages!
P(1)
P(2)
P(3)
28. 28
Use
distributed
sampling
protocol
in
EXP3.
Yields
distributed
single-‐sensor
selecRon
algorithm
Distributed
EXP3
Broadcast
the
change
of
weight
for
now
Distributed
EXP3
Theorem:
Exact
same
performance
as
centralized
EXP3
29. 29
Distributed
Online
Greedy
Distributed
Online
Greedy
(DOG)
selects
a
set
of
k
sensors
on
each
round,
using
Distributed
EXP3
as
a
subrouRne.
D-‐EXP3
D-‐EXP3
D-‐EXP3
Theorem
:
DOG
selects
sensors
St
that
obtain
Using
messages
per
round
in
expectaRon.
30. 30
SelecRon
techniques
extend
efficiently
to
non-‐broadcast
communicaRon
models.
CommunicaRon
Models
Star
Network
Model:
messages
between
base
staRon
and
one
sensor
are
unit
cost.
D-‐EXP3
samples
from
Each
sensor
needs
to
know
the
sum
of
all
weights
Lazy-‐DOG.
A
sensor
only
updates
its
sum
when
it
communicates
with
base
staRon.
Theorem:
Lazy-‐DOG
gives
same
selecRon
performance
as
DOG,
and
reduces
messages
in
star
model
from
N
to
log(N).
31. 31
ObservaRon-‐Dependent
SelecRon
Sensing
can
be
cheap
while
communicaRon
is
costly.
Can
current
observaRons
inform
selecRon?
Valuable
observaHon
Domain
knowledge
32. 32
ObservaRon-‐Dependent
SelecRon
2.
Sensor
v
acRvates
if
exceeds
a
threshold.
3.
Given
communicaRon
cost
C,
feed
back
OD-‐DOG.
A
sensor’s
current
measurement
can
influence
its
decision
to
acRvate.
1.
Each
sensor
v
esRmates
its
marginal
value
Learn
the
threshold
Useful
for
detecHng
important
and
rare
events
33. 33
Temperature
Monitoring
Select
10
from
46
temperature
sensors
deployed
at
Intel
Research
Berkeley.
SERVER
LAB
KITCHEN
COPYELEC
PHONEQUIET
STORAGE
CONFERENCE
OFFICEOFFICE
50
51
52 53
54
46
48
49
47
43
45
44
42 41
3739
38 36
33
3
6
10
11
12
13 14
15
16
17
19
20
21
22
2425
26283032
31
2729
23
18
9
5
8
7
4
34
1
2
35
40
OpRmize
the
expected
reducRon
in
mean
squared
predicRon
error
(EMSE).
(oten)
submodular*
34. 34
Temperature
Monitoring
Offline
greedy
Distributed
Online
Greedy
OpRmize
sensor
placement
for
monitoring
temperature
in
an
office
building.
Select
10
of
46
sensors.
35. 35
Outbreak
DetecRon
Ba<le
of
Water
Sensor
Networks:
Detect
contaminaRon
events
in
an
urban
water
distribuRon
network.
ObservaRon-‐dependent
selecRon
to
ensure
important
events
are
detected
ContaminaRon
models
provided
by
EPA
Submodular
36. 36
Outbreak
DetecRon
High
communicaHon
cost
Low
communicaHon
cost
Balances
added
value
and
communicaHon
cost
Greedy
0.1
avg.
extra
acHvaHons
5
avg.
extra
acHvaHons
OD-‐DOG
with
observaRon-‐dependent
selecRon
for
various
communicaRon
costs
C.
37. • DOG,
a
distributed
sensor
selecRon
algorithm
that
applies
to
many
sensing
applicaRons.
• Strong
theoreRcal
guarantees
on
performance
and
communicaRon
cost.
• OD-‐DOG
for
observaRon-‐specific
selecRon.
Can
incorporate
domain
knowledge.
• Performs
well
on
several
real
sensor
data
sets.
Conclusions
37
