Hueristics for efficient cooperation

-Ariel Gabizon-A.I seminar

•Coordination can be positive-saving work by cooperationor negative-2 robots avoiding bumping in to each other

•Efficiency in terms of computing the coordinated planand/or in terms of the communication during planning/execution

•Lecture is mainly about coordination of

individual plans of different agents.

Georgeff’s coordination algorithim

• Given 2 individual plans p1,p2 of agents a1,a2 create a plan for safe execution that’s as parallel as possible.

• For example in the blocks world it wouldn’t be safe for a1 to put block C on B if a2’s next action is to pick up B

Georgeff’s coordination algorithim

• Define S as the set of states.Then an action A is a function S-> S.

• Question:how to check if 2 actions :A,B can be executed in parallel.

• Problem : if an action is represented as a S->S function we don’t know what needs to hold during execution.

Georgeff’s coordination algorithim• Different representation:

• an action is a sequence of sets of states:

{[Domain],[Moment1],…,[Momentk],[Range]}

• The Domain set inclueds the states in which the action can be applied• The Moment sets describe the states the domain could go through while the

action is executed.• The range set includes the states that could be reached after action execution

Georgeff’s coordination algorithim• Given actions A= [p1,..,pm] and B = [q1,..qn] we want to check if they can be executed in

parallel.

• Since we don’t control the rate of action execution in each agent we have to check that all possible interleavings are safe.

• Example of interleaving:[p1,p2,q1,p3,q2,..qm,p4,..pm].

Georgeff’s coordination algorithim• More efficient:represent each set of states by a set of conditions so the Strips

assumption holds:What can’t be proved from the conditions hasn’t changed.• Now it’s enough to check that for each I and j <pi,qj> is satisfiable to know

that all interlevings are OK.In this case we say the actions A and B commute.

Georgeff’s coordination algorithim• Saving work in commutativity checks: We can do a lot of work only once per domain by

checking if action classes commute.• Example:<handempty,holding(X)> is not satisfiable for any value of X• The algoritihm:Ignore all parts of a plan that commute with the other plan and just synchronize

the other parts(similliar to O.S ciritical section techniques)

Focusing communication• Suppose we have a group of agents competing over a group of resources.• We want tp schedule resource usage without clashes• attempt 1 :each agent trys to build his schedule and communicates with other

agents to make sure their scheduls don’t match.

Focusing communication• More efficient:Assign an agent to each resource .• When an agent makes a demand for a resource inform him of all the demands made to that

resource.so he can coordinate himself with other requests• this method gives more information with less communication• similliar to the way the blackboard system focuses communication.

Coordinating at higher abstraction levels

• Example:agent Aj(j=1,2) needs to make repeated deleveries from Si to Ti

S1

S2

T1

T2

Coordinating at higher abstraction levels• Given plans:• A1:[turn right,go up,..,pick box…]• A2:[go left,turn right,…,pick box..]• we need to synchornize execution to make sure the agents don’t bump into each other.• Any coordination technique’s running time will probably depend on the plans’ length-if we could make the plans

shorter we could save time.

Coordinating at higher abstraction levels• Idea:have agents hold their plans at different levels of abstraction(which implies different levels of detail)• for example at a high level of abstraction the plans could be:• A1:[Use upper part of room from 12:00-14:00]• A2:[Use upper part of room from 12:00-14:00]• a solution in this abstraction level would have A2 using only the lower part of the room(or lower door)• tradeoff between coordination complexity and solution complexity

Coordinating at higher abstraction levels• Idea:have agents hold their plans at different levels of abstraction(which implies different levels of detail)• for example at a high level of abstraction the plans could be:• A1:[Use upper part of room from 12:00-14:00]• A2:[Use upper part of room from 12:00-14:00]• a solution in this abstraction level would have A2 using only the lower part of the room(or lower door)

Implicit cooperation

Example:TheTile World

A1 A2

h2

h1 Hi-holes

Ai-agents

lines-bariers

black squares

are tiles

• Agents can imporve preformancee through cooperation.

• But finding optimal multi-agent plan can be expensive.

• Can we approximate the optimal cooperative behaviour efficiently?

• Maybe without any explicit consideration of the agent interactions at all?

Cooperative state changing rules(Goldman,Rosenchein)

• Solution:Instead of trying to explicitly coordinate with other agents just do what you can to “Make the world a better place” without thinking about interaction with other agents.

Cooperative state changing rules(Goldman,Rosenchein)

In (relativley) more concrete terms:1)Find a quantitive characteristic of your

domain that ,in general,makes pursuing goals easier when it’s value is higher.

2)program agents with a meta-rule to take actions to increase this value in addition to their goal-directed actions

Cooperative state changing rules(Goldman,Rosenchein)

Example:

In the tile-wordls the characteristic is the

degree of freedom of the tiles.

The meta-rule is to take x additional actions to “free” tiles

x is the agents given coorperation level.

Focal Points-Coordination without Communication

Example:

• contestants have to seperatley decide how to divide 100 dolars into 2 piles.

• If both divide in the same way they get the prize.

Focal Points-Coordination without Communication

• People have meta-rules that channel their decisions to certain Focal Points beetween many seemingly equal alternatives.

• Focal points can be characterized by easily computable uniqueness,simmetry and extremeness.

Focal Points-Coordination without Communication

• If we could formalize this notion we could have agents using focal points to:

-coordinate without communication.

-improve interaction with humans.

Focal Points-Coordination without Communication

• Step logic can help with the notion of easily computable.

• A possible algorithim could be to go over a group of objects and choose the one with maximal rarity + extremness when you sum over the predicates in the enviorment

Example:TheTile World

A1 A2

h2

h1 Hi-holes

Ai-agents

lines-bariers

black squares

are tiles