Vicki Allan 2008 Looking for students for two NSF funded grants.
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Transcript of Vicki Allan 2008 Looking for students for two NSF funded grants.
Vicki Allan2008
Looking for students
for two NSF funded grants
Funded Projects 2008-2011
• CPATH – Computing Concepts– Educational– Curriculum Development– Looking for help in the creation of a new
introductory course – USU 1360
• COAL – Coalition Formation– Research in Multi-agent systems
CPATH• There is a need for more computer
science graduates.
• There is a lack of exposure to computer science.
• Introductory classes are unattractive to many.
• Women are not being attracted to computer science despite forces which should attract women – good pay, flexible hours, interesting problems.
Create a library of multi-function Interactive Learning
Modules (ILMs)
• Showcase computational thinking
• De-emphasize programming
The balls on the left are to be exchanged with the balls on the right by a sequence of moves. Any ball can move into adjacent empty slot. Any ball can jump over a single neighbor to an empty slot.
ComplexityAlgorithm designAbstraction – general purpose rules
Need Students
• Good programmers to program interactives. Using Java or flash.
• Ideas for how to revitalize undergraduate education
• TA for next semester to help with USU 1360
COAL
Second project involves multi-agent systems
If two heads are better than one, how about 2000?
Monetary Auction
• Object for sale: a dollar bill
• Rules– Highest bidder gets it– Highest bidder and the second highest bidder
pay their bids– New bids must beat old bids by 5¢.– Bidding starts at 5¢. – What would your strategy be?
Give Away
• Bag of candy to give away
• If everyone in the class says “share”, the candy is split equally.
• If only one person says “I want it”, he/she gets the candy to himself.
• If more than one person says “I want it”, I keep the candy.
The point?
• You are competing against others who are as smart as you are.
• If there is a “weakness” that someone can exploit to their benefit, someone will find it.
• You don’t have a central planner who is making the decision.
• Decisions happen in parallel.
Cooperation
• Hiring a new professor this year.
• Committee of three people to make decision
• Have narrowed it down to four.
• Each person has a different ranking for the candidates.
• How do we make a decision?
Binary ProtocolOne voter ranks c > d > b > aOne voter ranks a > c > d > bOne voter ranks b > a > c > d
winner (c, (winner (a, winner(b,d)))=awinner (d, (winner (b, winner(c,a)))=d
winner (d, (winner (c, winner(a,b)))=c
winner (b, (winner (d, winner(c,a)))=b
surprisingly, order of pairing yields different winner!
If you only wanted to find the first place winner, could you count the number of times a person was ranked first?
• a > b > c >d • a > b > c >d • a > b > c >d • a > b > c >d • b > c > d> a• b > c > d> a• b > c > d> aa=19, b=24, c=17,
d=10Just counting first ranks isn’t enough.
Borda protocol
assigns an alternative |O| points for the highest preference, |O|-1 points for the second, and so on
The counts are summed across the voters and the alternative with the highest count becomes the social choice
15
reasonable???
Borda Paradox
• a > b > c >d • b > c > d >a• c > d > a > b• a > b > c > d• b > c > d> a• c >d > a >b• a <b <c < da=18, b=19, c=20,
d=13
Is this a good way?
Clear loser
Borda Paradox – remove loser (d), winner changes
• a > b > c >d • b > c > d >a• c > d > a > b• a > b > c > d• b > c > d> a• c >d > a >b• a <b <c < da=18, b=19, c=20,
d=13
a > b > c b > c >a c > a > b a > b > c b > c > a c > a >b a <b <c
a=15,b=14, c=13
When loser is removed, second worst becomes winner!
Conclusion
• Finding the correct mechanism is not easy
Who Works Together in Agent Coalition Formation?
Vicki Allan – Utah State UniversityVicki Allan – Utah State University
Kevin Westwood – Utah State UniversityKevin Westwood – Utah State University
Presented September 2007, NetherlandsPresented September 2007, Netherlands
(Work also presented in Hong Kong, (Work also presented in Hong Kong, Finland, Australia, California)Finland, Australia, California)
CIA 2007CIA 2007
Overview
• Tasks: Various skills and numbers
• Agents form coalitions
• Agent types - Differing policies
• How do policies interact?
Multi-Agent Coalitions
• “A coalition is a set of agents that work together to achieve a mutually beneficial goal” (Klusch and Shehory, 1996)
• Reasons agent would join Coalition– Cannot complete task alone– Complete task more quickly
Skilled Request For Proposal (SRFP) Environment
Inspired by RFP (Kraus, Shehory, and Taase 2003)• Provide set of tasks T = {T1…Ti…Tn}
– Divided into multiple subtasks– In our model, task requires skill/level– Has a payment value V(Ti)
• Service Agents, A = {A1…Ak…Ap}– Associated cost fk of providing service– In the original model, ability do a task is determined probabilistically – no two agents alike.– In our model, skill/level– Higher skill is more flexible (can do any task with lower level skill)
Why this model?• Enough realism to be interesting
– An agent with specific skills has realistic properties.
– More skilled can work on more tasks, (more expensive) is also realistic
• Not too much realism to harm analysis– Can’t work on several tasks at once – Can’t alter its cost
Auctioning Protocol• Variation of a reverse auction
– One “buyer” lots of sellers– Agents compete for opportunity to perform services– Efficient way of matching goods to services
• Central Manager (ease of programming)1) Randomly orders Agents
2) Each agent gets a turn• Proposes or Accepts previous offer
3) Coalitions are awarded task
• Multiple Rounds {0,…,rz}
Agent Costs by Level
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10
Skill Level
Co
sts
General upward trend
05
10152025
3035
Agent 3 Agent 2 Agent 5
Costs
Agent Cost Profit
0
5
10
15
20
25
30
35
Agent 11 Agent 2 Agent 5
Costs
Agent Cost Profit
Agent costAgent costBase cost derived from skill and skill levelBase cost derived from skill and skill level Agent costs deviate from base cost Agent costs deviate from base cost
Agent paymentAgent paymentcost + proportional portion of net gaincost + proportional portion of net gain
Only Change in coalition
How do I decide what to propose?
The setup
• Tasks to choose from include skills needed and total pay
• List of agents – (skill, cost)
• Which task will you choose to do?
Decisions
If I make an offer…• What task should I propose doing?• What other agents should I
recruit?If others have made me an offer…• How do I decide whether to
accept?
Coalition Calculation Algorithms• Calculating all possible coalitions
– Requires exponential time– Not feasible in most problems in which
tasks/agents are entering/leaving the system
• Divide into two steps1) Task Selection
2) Other Agents Selected for Team– polynomial time algorithms
Task Selection- 4 Agent Types1. Individual Profit – obvious, greedy
approach
Competitive: best for me
Why not always be greedy?• Others may not accept – your membership is
questioned• Individual profit may not be your goal
2. Global Profit
3. Best Fit
4. Co-opetitive
Task Selection- 4 Agent Types
1. Individual Profit
2. Global Profit – somebody should do this task
I’ll sacrificeWouldn’t this always be a noble thing to do?• Task might be better done by others• I might be more profitable elsewhere
3. Best Fit – uses my skills wisely
4. Co-opetitive
Task Selection- 4 Agent Types1. Individual Profit
2. Global Profit
3. Best Fit – Cooperative: uses skills wisely
Perhaps no one else can do it
Maybe it shouldn’t be done
4. Co-opetitive
4th type: Co-opetitive Agent
• Co-opetition– Phrase coined by business professors
Brandenburger and Nalebuff (1996), to emphasize the need to consider both competitive and cooperative strategies.
• Co-opetitive Task Selection– Select the best fit task if profit is within P% of
the maximum profit available
What about accepting offers?Melting – same deal gone later
• Compare to what you could achieve with a proposal
• Compare best proposal with best offer
• Use utility based on agent type
Some amount of compromise is necessary…
We term the fraction of the total possible you demand – the compromising ratio
Resources Shrink
• Even in a task rich environment the number of tasks an agent has to choose from shrinks– Tasks get taken
• Number of agents shrinks as others are assigned
Resources Task Rich
010
2030
4050
6070
80
1 2 3 4 5 6 7 8 9 10 11 12
Rounds
Availab
le R
eso
urc
es
My Tasks
Total Tasks
Total Agents
My tasks parallel total tasks
Task Rich: 2 tasks for every agent
Scenario 1 – Bargain Buy
• Store “Bargain Buy” advertises a great price
• 300 people show up
• 5 in stock
• Everyone sees the advertised price, but it just isn’t possible for all to achieve it
Scenario 2 – selecting a spouse
• Bob knows all the characteristics of the perfect wife
• Bob seeks out such a wife
• Why would the perfect woman want Bob?
Scenario 3 – hiring a new PhD
• Universities ranked 1,2,3
• Students ranked a,b,c
Dilemma for second tier university
• offer to “a” student
• likely rejected
• delay for acceptance
• “b” students are gone
Affect of Compromising Ratio
• equal distribution of each agent type
• Vary compromising ratio of only one type (local profit agent)
• Shows profit ratio = profit achieved/ideal profit (given best possible task and partners)
Local Profit Agents (Task Rich)
0
0.1
0.2
0.3
0.4
0.5
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Compromising Ratio of Local Profit
Pro
fit/
Idea
l Agent/Task .5
Agent/Task 1
Agent/Task 2
Agent/Task 3
Achieved/theoretical bestNote how profit is affect by load
Profit only of scheduled agents
Scheduled Agent Profit (Task Rich)
0.440.46
0.480.5
0.520.54
0.560.58
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
Compromising Ratio of Local Profit
Pro
fit/
Idea
l LocalProf
GlobProf
Coopet
BestFit
Only Local Profit agentschange compromising ratio
Yet others slightly increase too
Note
• Demanding local profit agents reject the proposals of others.
• They are blind about whether they belong in a coalition.
• They are NOT blind to attributes of others.
• Proposals are fairly good
Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
For every agent type, the most likely proposer For every agent type, the most likely proposer was a Local Profit agent.was a Local Profit agent.
Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
No reciprocity: Coopetitive eager to accept Local Profit proposals, No reciprocity: Coopetitive eager to accept Local Profit proposals, but Local Profit agent doesn’t acceptbut Local Profit agent doesn’t acceptCoopetitive proposals especially wellCoopetitive proposals especially well
Balanced Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
Rat
io t
o E
xpec
ted
LocalProf
GlobProf
Coopet
BestFit
For every agent type,For every agent type,Best Fit is a strong acceptor.Best Fit is a strong acceptor.
Perhaps because it isn’t accepted well as a proposerPerhaps because it isn’t accepted well as a proposer
Coopetitive agents function better as proposers to Local Profit agents in balanced or task rich environment.– When they have more choices, they tend to
propose coalitions local profit agents like– More tasks give a Coopetitive agent a better
sense of its own profit-potential
Load balance seems to affect rolesLoad balance seems to affect roles
Coopetitive Agents look Coopetitive Agents look at fit as long as it isn’t too bad at fit as long as it isn’t too bad
compared to profit.compared to profit.
Agent rich: 3 agents/task
Agent Rich Proposers
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
LocalProf GlobProf Coopet BestFit
LocalProf
GlobProf
Coopet
BestFit
Coopetitive accepts most proposals Coopetitive accepts most proposals from agents like itselffrom agents like itself
in agent rich environmentsin agent rich environments
• Do agents generally want to work with agents of the same type? – Would seem logical as agents of the same
type value the same things – utility functions are similar.
– Coopetitive and Best Fit agents’ proposal success is stable with increasing percentages of their own type and negatively correlated to increasing percentages of agents of other types.
Look at function with increasing numbers of one other type.
Local Profit, Task Rich
0123456
Proposers
Joiners
What happens as we change relative percents of each agent?
• Interesting correlation with profit ratio.
• Some agents do better and better as their dominance increases. Others do worse.
Individual Profit Ratio (std dev 5)
0.58
0.59
0.6
0.61
0.62
0.63
0.64
0% 20% 40% 60% 80% 100%
Agent %
Ind
ivid
ual
Pro
fit
Rat
io
Individual Profit
Global Profit
Best Fit
Co-opetitive
shows relationship if all shows relationship if all equal percentequal percent
Best fit Best fit does better does better and better and better as more as more
dominant in dominant in setset
Best fit Best fit does better does better and better and better as more as more
dominant in dominant in setset
Local ProfitLocal Profitdoes better whendoes better whenit isn’t dominantit isn’t dominant
So who joins and who proposes?
• Agents with a wider range of acceptable coalitions make better joiners.
• Fussier agents make better proposers.
• However, the joiner/proposer roles are affected by the ratio of agents to work.
Conclusions
• Some agent types are very good in selecting between many tasks, but not as impressive when there are only a few choices.
• In any environment, choices diminish rapidly over time.
• Agents naturally fall into role of proposer or joiner.
Future Work
• Lots of experiments are possible
• All agents are similar in what they value. What would happen if agents deliberately proposed bad coalitions?