Analyzing the Performance of Randomized Information Sharing under Noise and Dynamics

transcript

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

Gossip

• Agent pushes information probabilistically to subset of neighbors

Random Token Routing

• Agent pushes information to a single random neighbor

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

“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

Optimality of n-step lookahead

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

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)

Normal distribution performance

Exponential distribution performance

Noise effects on lookahead policy

Network Density Effects

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

Analyzing the Performance of Randomized Information Sharing under Noise and Dynamics

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