online distributed sensor selection daniel golovin, matthew faulkner, andreas krause rsrg...
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Online Distributed Sensor Selection
Daniel Golovin, Matthew Faulkner, Andreas Krause
rsrg @caltech..where theory and practice
collide1
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Sensor-equipped cell phones are ubiquitous.
Which sensors should send data?
Can current measurements inform selection?
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Community Sensing
Used for traffic monitoring, pollution detection, earthquake measurement.
Constraints on bandwidth, power, privacy… Impractical 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 Selection Problem
People Detected:
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Duplicates only counted once
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Set V of sensors, |V| = NSelect a set of k sensors Sensing quality model
Typically NP-hard…
A Sensor Selection Problem
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SubmodularityDiminishing returns property for adding more sensors.
Many objectives are submodular:Detection, coverage, mutual information, and others.
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For all , and a sensor ,
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Lets choose sensors S = {v1 , … , vk} greedily
[Nemhauser et al ‘78] If F is submodular, the Greedy algorithm gives constant factor approximation:
Greedy Selection
1. Must know sensing model F2. Greedy is centralized3. Selection ignores current
sensor values6
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Online Sensor SelectionGet to choose sensors on each round t. Then is revealed.
Need to explore different sets.
Only need to evaluate F for chosen sets.
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Online Sensor SelectionGet to choose sensors on each round t. Then is revealed.
Round 1Round 2Round 3
Only assume is submodular and bounded
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Online Greedy SelectionAt 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 fixed optimum:
Single Sensor Selection
EXP3 [Auer et al ‘95]
balances exploring and exploiting
Can we avoid centralized sampling?
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Idea: Independent draws until exactly one sensor broadcasts a success.
Distributed Sampling
Doesn’t sample from correct distribution
P(1) P(2) P(3)
Centralized sampling may not scale practically.
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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 distribution, while using few messages!
P(1) P(2) P(3)
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Use distributed sampling protocol in EXP3. Yields distributed single-sensor selection 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 GreedyDistributed Online Greedy (DOG) selects a set of k sensors on each round, using Distributed EXP3 as a subroutine.
D-EXP3 D-EXP3 D-EXP3
Theorem : DOG selects sensors St that obtain
Using messages per round in expectation.
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Selection techniques extend efficiently to non-broadcast communication models.
Communication Models
Star Network Model: messages between base station 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 station.
Theorem: Lazy-DOG gives same selection performance as DOG, and reduces messages in star model from N to log(N).
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Observation-Dependent SelectionSensing can be cheap while communication is costly. Can current observations inform selection?
Valuable observation Domain
knowledge
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Observation-Dependent Selection
2. Sensor v activates if exceeds a threshold.
3. Given communication cost C, feed back
OD-DOG. A sensor’s current measurement can influence its decision to activate.
1. Each sensor v estimates its marginal value
Learn the threshold
Useful for detecting important and rare events
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Temperature MonitoringSelect 10 from 46 temperature sensors deployed at Intel Research Berkeley.
SERVER
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PHONEQUIET
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Optimize the expected reduction in mean squared prediction error (EMSE).
(often) submodular*
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Temperature Monitoring
Offline greedy
Distributed Online Greedy
Optimize sensor placement for monitoring temperature in an office building. Select 10 of 46 sensors.
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Outbreak DetectionBattle of Water Sensor Networks: Detect contamination events in an urban water distribution network.
Observation-dependent selection to ensure important events are detected
Contamination models provided by EPA
Submodular
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Outbreak Detection
High communication
cost
Low communication cost
Balances added value and communication cost
Greedy
0.1 avg. extra activations
5 avg. extra activations
OD-DOG with observation-dependent selection for various communication costs C.
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• DOG, a distributed sensor selection algorithm that applies to many sensing applications.
• Strong theoretical guarantees on performance and communication cost.
• OD-DOG for observation-specific selection. Can incorporate domain knowledge.
• Performs well on several real sensor data sets.
Conclusions
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