Coordination

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Coordination

• Gaia Varese

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Paper

• Coordination without Communication Experimental
  Validation of Focal Point Techniques
• Authors
• Maier Fenster
• Sarit Kraus
• Jeffrey S. Rosenschein
• In Proceedings of the First International
  Conference on Multiagent Systems (1995)

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The problem

• Coordination without communication

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Coordination

• How to coordinate the actions of different agents
  in order to reach a mutual benefit
• Some problems
• Each agent has its own perception of the world
• Each agent has its own goals

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Why coordination without communication?

• Communication is expensive
• Agents are loosely coupled
• Communication is sometimes impossible
• Radiofrequency disturbance
• Communication is cut off
• Communication is sometimes not advisable
• Secrecy demands

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Objective

• Making the involved agents come to an agreement
  with little or no communication

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Intuition

• People are capable of sophisticated interaction
  with little explicit communication!

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Example

• Agents two people
• They both have to decide how to divide 100
  identical objects in two piles
• They must try to match the decision of the other
  one
• They cannot communicate!

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Some of the possible choices
90
100
75
75
75
60
40
50
25
25
25
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Pile 1
Pile 2
Pile 1
Pile 2
Pile 1
Pile 2
Pile 1
Pile 2
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Which is the best choice?

• The one that have the highest probability to match

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Which is the best choice?
100
75
50
50
50
25
Pile 1
Pile 2
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Another example

• Choose a positive number!
• You must try to match the choice of another
  person!

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Which is the best choice?

• 1

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How people choose the best solution?

• Despite surface equivalence among many solutions,
  people use some common sense to choose a specific
  solution
• They use heuristics
• Uniqueness
• Symmetry
• Extremeness

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How to make automated agents behave like people?

• Automated agents do not have common sense!
• Solution create an algorithm capable of
  automatically identifying the best solution,
  using the same heuristics used by people

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Focal points

• Focal points best solutions
• Introduced by Schelling in the 1963

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The focal point algorithm

• Two (or more) agents are trying to choose the
  same object out of a set of objects
• They cannot communicate!
• Objective automatically identifying focal points
  in a given world
• Focal points special objects belonging to
  that given world ? Heuristics
• Rarity
• Extremeness

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Features of the world

• A set of objects out of which the agents must
  choose one (the same one!)
• A set of object properties
• A set of values for each object property

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How to identify focal points?

• For each object belonging to the given world, a
  focal point value is calculated, taking into
  account
• its rarity
• its extremeness

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How to evaluate the rarity of an object?

• How rare are the values that the object assumes
  on its properties?
• How many objects in the world share the same
  values?

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How to evaluate the extremeness of an object?

• How close are the values that the object assumes
  on its properties to one of the extreme values
  that each property can take?
• Note the extremeness evaluation is useful only
  if the values of a property can be ordered
• Example 1 small, medium, big, huge
• Example 2 1, 2, 3, 4, 5,

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Choosing the solution

• Each agent must choose the object with the
  largest focal point value that is unique in
  having that value
• If such object exists ? The algorithm succeeds ?
  The agents will meet!
• If such object does not exist ? The algorithm
  fails ? The agents will not find an agreement
• Note the number of agents is not important!

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When does the algorithm is expected to work?

• When any characteristic of an object can be
  encoded in the values its properties can take
• When the agents observe the same objects and
  properties in the world
• When all the agents use this algorithm!

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Testing

• Evaluation of the algorithm success rate over
  various randomly generated worlds
• Randomly generated worlds may change in
• the number of objects
• the number of properties
• the number of values for each property
• the distribution of property values (e.g.,
  binomial distribution, uniform distribution)

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Results

• In general, the success rate of the algorithm
  rises as
• the number of objects increases
• the number of properties increases
• the number of values increases
• With few objects and properties
• rarity is not so meaningful
• With few property values
• extremeness is not so meaningful

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Taking into account both rarity and extremeness

• Success rate gt 97 with
• at least 3 objects
• at least 2 properties

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Taking into account only rarity

• If the property values cannot be ordered
• Success rate gt 97 with
• at least 7 objects
• at least 5 properties

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Pros of the algorithm

• Coordination without communication
• High success rate
• Easy
• Low complexity
• Domain independent
• Representation independent
• Agents can use different names for denoting the
  same object, the same property or the same value

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Cons of the algorithm

• Low success rate with
• a low number of objects
• a low number of properties
• It does not take into account the relative
  importance of properties in calculating the
  rarity of an object
• Some specific properties are more important than
  others in stating the rarity of an object

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Improvements

• Even if the algorithm fails, the focal point
  choice can be done between a subset of objects
• The importance of each property can be
  calculated and taken into account (in the real
  world)