Analyzing the Performance of Randomized Information Sharing

under Noise and Dynamics

Paul Scerri,Prasanna Velagapudi,

Katia Sycara

Robotics InstituteCarnegie Mellon University

Large Multiagent Teams

• 1000s of robots, agents, and people• Must collaborate to complete complex tasks• Necessitate distributed algorithms• Assuming peer-to-peer communication model

Information Sharing

• How do we deliver information efficiently?– Get to the people that need it most– Don’t waste communication bandwidth

• Key Idea: Different agents have different utility for a single piece of information!

Information Sharing

• How do we measure information need?– “Need” is domain-specific– Define a utility function for each agent which is

maximized when it receives the information it needs

Existing Approaches

• Simple– Flooding– Gossip– Tokens

• Intelligent– STEAM– Channel Filtering– Particle Filter exchange

Classical Flooding

• Agent pushes information to every neighbor

Info

Info Info

Info

Info

Gossip

• Agent pushes information probabilistically to subset of neighbors

Info

Info

Info

Random Token Routing

• Agent pushes information to a single random neighbor

Info

Problem

• When are intelligent strategies necessary?– Complexity adds overhead– In many simple domains, random policies work

• Is there a set of problem characteristics that can predict algorithm performance?

“Optimal” performance

• Simplest case: – Single piece of information– Static network

• Optimal algorithm for a fully connected network:– Use first transmission to get to agent with the highest

utility for the information– Use second transmission to get to agent with second

highest utility, etc.

[Velagapudi et al., AAMAS 2009]

“Optimal” performance

• Suppose distribution of utility over network can be approximated by a well-known distribution– Expected utility of the optimal algorithm for k

transmissions is sum of k highest order statistics– Forms upper bound on performance for partially

connected networks with same utility distribution

[Velagapudi et al., AAMAS 2009]

“Optimal” performance• In partially connected networks, analytic expression for

optimality is much harder to compute

• For the class of token algorithms, approximate the optimal token policy using an n-step lookahead policy:– Assume we have some estimate of utility for every other

node (possibly with noise)1. Exhaustively search all n-length paths from current node2. Send information along best path3. Repeat until TTL reaches 0

[Velagapudi et al., AAMAS 2009]

Optimality of n-step lookahead

[Velagapudi et al., AAMAS 2009]

2-step lookahead: pathological case?

Experimental Setup

• Objective:– Study effects of network properties on optimality of

random token routing

• Single piece of information (token)• Static networks– Scale-Free, Small Worlds, Hierarchical, Lattice,

Random• Agents’ utilities sampled from utility distribution– Normal, Exponential

[Velagapudi et al., AAMAS 2009]

Experimental Setup

• Algorithms:– Random:

• Send to random neighbor each time step

– RandomSelfAvoid• Send to random neighbor that has not already been visited

– RandomTrails• Send to random neighbor using an edge that was not

previously used

– Lookahead• 4-step lookahead policy (as previously described)

[Velagapudi et al., AAMAS 2009]

Normal distribution performance

[Velagapudi et al., AAMAS 2009]

Exponential distribution performance

[Velagapudi et al., AAMAS 2009]

Noise effects on lookahead policy

[Velagapudi et al., AAMAS 2009]

Network Density Effects

[Velagapudi et al., AAMAS 2009]

Summary of Previous Work

• Random policies perform reasonably under certain utility distributions

• Adding simple heuristics significantly improves performance

• Certain networks are more conducive to randomized methods

• As noise is added, gap between random and optimal policies closes

Multiple token interaction

• How does performance change when systems are generating many tokens with redundant information?

• If noise is added, are dynamic systems affected differently than static systems?

Experimental Setup

• Scale-free network of 50 agents• Token time-to-live (TTL) of 20• Objective: minimize variance– Cost modeled as sum of “covariance” over time– “Covariance” update rules approximate 1D

Kalman filter update

Dynamic Effects

Noise Effects

Discussion

• Significant difference in performance between random and lookahead policies

• Intelligent heuristics may be able to help in dynamic and noisy situations