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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
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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
Motivation • Large, heterogeneous teams of agents • 1000s of robots, agents, and people • Must collaborate to complete complex tasks • Necessarily decentralized algorithms Search and Rescue UAV Surveillance Disaster Response AAMAS 2009, Budapest
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 Tokens Gossip STEAM DDF Matchmakers Dec-POMDP Flooding Complexity Communication AAMAS 2009, Budapest
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
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
Problem • Maximize team performance: utility communication agents info. source dissemination tree AAMAS 2009, Budapest
Problem • How helpful is knowledge of utility? optimal w/out network full knowledge Utility no knowledge Communications costs AAMAS 2009, Budapest
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
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
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
How well can we do? • Lookahead policy • Estimate of performance given complete local knowledge • Exhaustive n-step search over possible routes AAMAS 2009, Budapest
Optimality of “smart” algorithms pathological case AAMAS 2009, Budapest
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
Randomized optimality large performance gap small performance gap AAMAS 2009, Budapest
Randomized optimality Normal Distribution Exponential Distribution AAMAS 2009, Budapest
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
Scaling effects • How does optimality of randomized strategies change with network size? AAMAS 2009, Budapest
Scaling effects • Scale-invariant for large team sizes AAMAS 2009, Budapest
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
Modeling maze navigation AAMAS 2009, Budapest
Modeling maze navigation False paths Frequency AAMAS 2009, Budapest
Modeling maze navigation AAMAS 2009, Budapest
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
Questions? AAMAS 2009, Budapest
Exp. 2: Randomized optimality AAMAS 2009, Budapest
Exp. 2: Randomized optimality AAMAS 2009, Budapest
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
Exp. 3: Noisy estimation AAMAS 2009, Budapest
Exp. 4: Structural properties • How is optimality affected by problem structure? • Network density • Distribution variance AAMAS 2009, Budapest
Exp. 4: Structural properties AAMAS 2009, Budapest
Exp. 4: Structural properties AAMAS 2009, Budapest
