Analyzing the Performance of
Randomized Information Sharing
Prasanna Velagapudi, Katia Sycara and Paul Scerri
Robotics Institute, Carnegie Mellon University
Oleg Prokopyev
Dept. of Industrial Engineering, University of Pittsburgh
AAMAS 2009, Budapest
1
Motivation
• Large, heterogeneous teams of agents
– 1000s of robots, agents, and people
– Must collaborate to complete complex tasks
– Necessarily decentralized algorithms
AAMAS 2009, Budapest
2
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
Related Work
Imprecision
Complexity
Communication
AAMAS 2009, Budapest
4
A simple example
• Two robots (1 static, 1 mobile)
• Mobile robot is planning path to goal point
goal
static
robot
mobile
robot
AAMAS 2009, Budapest
5
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
AAMAS 2009, Budapest
6
Problem
• Maximize team performance:
utility
info. source
communication
agents
dissemination tree
AAMAS 2009, Budapest
7
Problem
• How helpful is knowledge of utility?
optimal w/out network
full knowledge
Utility
no knowledge
Communications
costs
AAMAS 2009, Budapest
8
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
AAMAS 2009, Budapest
9
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
AAMAS 2009, Budapest
10
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
AAMAS 2009, Budapest
11
How well can we do?
• Lookahead policy
– Estimate of performance given complete local
knowledge
– Exhaustive n-step search over possible routes
AAMAS 2009, Budapest
12
Optimality of “smart” algorithms
pathological
case
AAMAS 2009, Budapest
13
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)
AAMAS 2009, Budapest
14
Randomized optimality
large
performance
gap
AAMAS 2009, Budapest
small
performance
gap
15
Randomized optimality
Normal Distribution
Exponential Distribution
AAMAS 2009, Budapest
16
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
AAMAS 2009, Budapest
17
Scaling effects
• How does optimality of randomized strategies
change with network size?
AAMAS 2009, Budapest
18
Scaling effects
• Scale-invariant for large team sizes
AAMAS 2009, Budapest
19
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?
AAMAS 2009, Budapest
20
Modeling maze navigation
AAMAS 2009, Budapest
21
Modeling maze navigation
Frequency
False paths
AAMAS 2009, Budapest
22
Modeling maze navigation
AAMAS 2009, Budapest
23
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)
AAMAS 2009, Budapest
24
Questions?
AAMAS 2009, Budapest
25
AAMAS 2009, Budapest
26
Exp. 2: Randomized optimality
AAMAS 2009, Budapest
27
Exp. 2: Randomized optimality
AAMAS 2009, Budapest
28
Exp. 3: Noisy estimation
• How does a global knowledge algorithm
degrade as estimates of utility become noisy?
• Gaussian noise scaled by network distance:
AAMAS 2009, Budapest
29
Exp. 3: Noisy estimation
AAMAS 2009, Budapest
30
Exp. 4: Structural properties
• How is optimality affected by problem
structure?
– Network density
– Distribution variance
AAMAS 2009, Budapest
31
Exp. 4: Structural properties
AAMAS 2009, Budapest
32
Exp. 4: Structural properties
AAMAS 2009, Budapest
33