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Analyzing the Performance of Randomized Information Sharing

Prasanna Velagapudi, Katia Sycara and Paul ScerriRobotics Institute, Carnegie Mellon University

Oleg ProkopyevDept. of Industrial Engineering, University of Pittsburgh

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Motivation

• Large, heterogeneous teams of agents– 1000s of robots, agents, and people– Must collaborate to complete complex tasks– Necessarily decentralized algorithms

Motivation

• Agents need to share information about objects and uncertainty in the environment to perform roles– Individual sensor readings unreliable– Used to reason about appropriate actions– Maintenance of mutual beliefs is key

• Need effective means to identify and disseminate useful information– Agent needs for information change dynamically– Highly redundant data

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Related WorkImprecision

Complexity Communication

Dec-POMDP

DDF

GossipSTEAM

Flooding

Matchmakers

Tokens

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• Two robots (1 static, 1 mobile)• Mobile robot is planning path to goal point

A simple example

static robot

mobile robot

goal

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Problem

• Utility: the change in team performance when an agent gets a piece of information

• Communication cost: the cost of sending a piece of information to a specific agent

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Problem

• Maximize team performance:utility communication

agentsinfo. source

dissemination tree

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Problem

• How helpful is knowledge of utility?

optimal w/out network

full knowledge

no knowledge

Utility

Communications costs

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Problem

• How can we compute the utility of information in a domain?

• Utility distribution– Model the distribution of utility over agents and

sample from that distribution to estimate utility

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Experiment

• Single piece of information shared each trial• Network of agents with utility sampled from

distribution

Distributions:• Normal• Exponential

Networks:• Small-Worlds (Watts Beta)• Scale-free (Preferential attachment)• Lattice (2D grid)• Hierarchy (Spanning tree)• Random

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How well can we do?

• Order statistic: expectation of k-th highest value over n samples– Computable for many common distributions

• Expected best case performance – How much utility could the information have over

a team of n agents?– Sum of k highest order statistics

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How well can we do?

• Lookahead policy– Estimate of performance given complete local

knowledge– Exhaustive n-step search over possible routes

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Optimality of “smart” algorithms

pathologicalcase

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How simple can we be?

• Random: Pass info. to randomly chosen neighbor

• Random Self-Avoiding– Keep history of agents visited– O(lifetime of tokens)

• Random Trail– Keep history of links used– O(# of tokens/time step)

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Randomized optimalitylarge

performance gap

small performance

gap

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Randomized optimalityNormal Distribution Exponential Distribution

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When is random competitive?

• Random policies can be useful in where:– Network structure is conducive– Distribution of utility is low-variance– Estimation of value is poor

• Maintaining shared knowledge is expensive

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Scaling effects

• How does optimality of randomized strategies change with network size?

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Scaling effects

• Scale-invariant for large team sizes

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Modeling maze navigation

• Mobile robots planning paths to goal points

• How would a randomized algorithm perform if this were taking place in a large team?

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Modeling maze navigation

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Modeling maze navigation

Freq

uenc

y

False paths

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Modeling maze navigation

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Conclusions

• Random policies are competitive under certain problem structures

• Information has different utility to each agent– Can lead to changes in actions/performance– Utility distributions: a mechanism to test information

sharing performance in large systems• Future work

– Validate utility distribution approximation– Effects of utility estimation error and dynamics– Better solution for optimal sharing (PCSTP)

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Questions?

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Exp. 2: Randomized optimality

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Exp. 2: Randomized optimality

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Exp. 3: Noisy estimation

• How does a global knowledge algorithm degrade as estimates of utility become noisy?

• Gaussian noise scaled by network distance:

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Exp. 3: Noisy estimation

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Exp. 4: Structural properties

• How is optimality affected by problem structure?– Network density– Distribution variance

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Exp. 4: Structural properties

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Exp. 4: Structural properties