AAMAS 2009, Budapest1 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

Motivation Large, heterogeneous teams of agents –1000s of robots, agents, and people –Must collaborate to complete complex tasks –Necessarily decentralized algorithms AAMAS 2009, Budapest2

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 AAMAS 2009, Budapest4 Imprecision Complexity Communication

Two robots (1 static, 1 mobile) Mobile robot is planning path to goal point A simple example AAMAS 2009, Budapest5 static robot mobile robot goal

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, Budapest6

Problem AAMAS 2009, Budapest7 Maximize team performance: utilitycommunication agents info. source dissemination tree

Problem How helpful is knowledge of utility? AAMAS 2009, Budapest8 optimal w/out network full knowledge no knowledge Utility Communications costs

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, Budapest9

Experiment Single piece of information shared each trial Network of agents with utility sampled from distribution AAMAS 2009, Budapest10 Distributions: Normal Exponential Networks: Small-Worlds (Watts Beta) Scale-free (Preferential attachment) Lattice (2D grid) Hierarchy (Spanning tree) Random

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, Budapest11

How well can we do? Lookahead policy –Estimate of performance given complete local knowledge –Exhaustive n-step search over possible routes AAMAS 2009, Budapest12

Optimality of “smart” algorithms AAMAS 2009, Budapest13 pathological case

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, Budapest14

Randomized optimality AAMAS 2009, Budapest15 large performance gap small performance gap

Randomized optimality AAMAS 2009, Budapest16 Normal DistributionExponential Distribution

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, Budapest17

Scaling effects How does optimality of randomized strategies change with network size? AAMAS 2009, Budapest18

Scaling effects AAMAS 2009, Budapest19 Scale-invariant for large team sizes

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, Budapest20

Modeling maze navigation AAMAS 2009, Budapest21

Modeling maze navigation AAMAS 2009, Budapest22 Frequency False paths

Modeling maze navigation AAMAS 2009, Budapest23

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, Budapest24

Questions? AAMAS 2009, Budapest25

AAMAS 2009, Budapest26

Exp. 2: Randomized optimality AAMAS 2009, Budapest27

Exp. 2: Randomized optimality AAMAS 2009, Budapest28

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, Budapest29

Exp. 3: Noisy estimation AAMAS 2009, Budapest30

Exp. 4: Structural properties How is optimality affected by problem structure? –Network density –Distribution variance AAMAS 2009, Budapest31

Exp. 4: Structural properties AAMAS 2009, Budapest32

Exp. 4: Structural properties AAMAS 2009, Budapest33