20140419 kawajiri m1gp

Online Distributed Sensor Selection,Daniel Golovin, Matthew Faulkner, Andreas Krause,

IPSN2010

2014/04/19 M1GP 1

Intelligent Cooperative Systems Lab. The University of TokyoICS

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(Sensor Selection)

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[Streeter & Golovin 08]: Online Greedy (OG)

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Intelligent Cooperative Systems Lab. The University of TokyoICS 7

[Auer et al 95]: EXP3

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EXP3 [Auer et al 95]


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P(1) P(2) P(3)


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: EXP3 4 P(1) P(2) P(3)


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Oine greedy

Distributed Online Greedy

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() A. Krause : NIPS, ICML, IPSN, IROS, ICRA, CVPR,

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Tutorial Andreas Krause http://submodularity.org/

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Online Distributed Sensor SelecRon

Daniel Golovin, MaUhew Faulkner, Andreas Krause

rsrg @caltech ..where theory and practice collide 16

Sensor-equipped cell phones are ubiquitous.

Which sensors should send data?

Can current measurements inform selecHon?

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Community Sensing

Used for trac monitoring, polluRon detecRon, earthquake measurement.

Constraints on bandwidth, power, privacy ImpracRcal to query all phones.

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Select two cameras to query, in order to detect the most people.

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A Sensor SelecRon Problem

People Detected:

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Duplicates only counted once

Set V of sensors, |V| = N Select a set of k sensors Sensing quality model

Typically NP-hard

A Sensor SelecRon Problem

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Submodularity Diminishing returns property for adding more sensors.

Many objec0ves are submodular: DetecRon, coverage, mutual informaRon, and others.

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For all , and a sensor ,

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

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Online Sensor SelecRon Get to choose sensors on each round t. Then is revealed.

Need to explore dierent sets.

Only need to evaluate F for chosen sets.

2 3 2

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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

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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?

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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 xed opRmum:

Single Sensor SelecRon

EXP3 [Auer et al 95]

balances exploring and exploiRng

Can we avoid centralized sampling?

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Idea: Independent draws unRl exactly one sensor broadcasts a success.

Distributed Sampling

Doesnt sample from correct distribuHon

P(1) P(2) P(3)

Centralized sampling may not scale pracRcally.

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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)

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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

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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.

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SelecRon techniques extend eciently 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).

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ObservaRon-Dependent SelecRon Sensing can be cheap while communicaRon is costly. Can current observaRons inform selecRon?

Valuable observaHon Domain

knowledge

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ObservaRon-Dependent SelecRon

2. Sensor v acRvates if exceeds a threshold.

3. Given communicaRon cost C, feed back

OD-DOG. A sensors current measurement can inuence its decision to acRvate.

1. Each sensor v esRmates its marginal value

Learn the threshold

Useful for detecHng important and rare events

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Temperature Monitoring Select 10 from 46 temperature sensors deployed at Intel Research Berkeley.

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OpRmize the expected reducRon in mean squared predicRon error (EMSE).

(oten) submodular*

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Temperature Monitoring

Oine greedy

Distributed Online Greedy

OpRmize sensor placement for monitoring temperature in an oce building. Select 10 of 46 sensors.

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Outbreak DetecRon Ba

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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.

DOG, a distributed sensor selecRon algorithm that applies to many sensing applicaRons.

Strong theoreRcal guarantees on performance and communicaRon cost.

OD-DOG for observaRon-specic selecRon. Can incorporate domain knowledge.

Performs well on several real sensor data sets.

Conclusions

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20140419 kawajiri m1gp

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