Robot Exploration with Combinatorial Auctions
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Transcript of Robot Exploration with Combinatorial Auctions
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http://www.sciencedaily.com/releases/2007/06/070609112916.htm
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Robot Exploration
with Combinatorial AuctionsM. Berhault, H. Huang, P. Keskinocak,
S. Koenig, W. Elmaghraby, P. Griffin, A. Kleywegt
http://www.news.cornell.edu/releases/rover/Mars.update8-19-04.html
Corey A. Spitzer - CSCI 8110 04-20-2010
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Optimal Task Allocation
Repeat Auctions
+
Combinatorial Auctions
+
Bidding Strategy
=
Near Optimal Allocation
http://shirt.woot.com/Derby/Entry.aspx?id=30206
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Repeat Auctions
Robot1
Robot2
Goal
UnknownTerrain
Wall
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Repeat Auctions
Robot1
Robot2
Goal
UnknownTerrain
Wall
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Repeat Auctions
Robot1
Robot2
Goal
Wall
Wall
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Repeat Auctions
Robot1
Robot2
Goal
Wall
Wall
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Single Item vs. Combinatorial Auctions
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Single Item vs. Combinatorial AuctionsPossible Bundles:
{}
{G1}
{G2}
{G3}
{G4}
{G1, G2}
{G1, G3}
{G1, G4}
{G2, G3}
{G2, G4}
{G3, G4}
{G1, G2, G3}
{G1, G2, G4}
{G1, G3, G4}
{G2, G3, G4}
{G1, G2, G3, G4}
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Task Synergies - Positive
Travel Distance for R1: T(S)
T({G3}) = 4
T({G4}) = 4
T({G3, G4}) = 7
T({G3, G4}) ≤ T({G3}) + T({G4})
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Task Synergies - Negative
Travel Distance for R1: T(S)
T({G3}) = 4
T({G1}) = 8
T({G3, G1}) = 12
T({G3, G1}) ≥ T({G3}) + T({G1})
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Bidding Strategies
Single
Three-Combination
Smart-Combination
Nearest-Neighbor
Graph-Cut
http://blog.handbagsmaster.com/index.php/2009/09/eleven-auction-terms-you-should-know/
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Bidding Strategies - Single
Same as single item auction
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Bidding Strategies - Three-CombinationPossible Bundles with 5 Goals:{}{G1}{G2}{G3}{G4}{G5}{G1, G2}{G1, G3}{G1, G4}{G1, G5}{G2, G3}{G2, G4}{G2, G5}{G3, G4}{G3, G5}{G4, G5}{G1, G2, G3}{G1, G2, G4}{G1, G2, G5}{G1, G3, G4}
{G1, G3, G5}{G1, G4, G5}{G2, G3, G4}{G2, G3, G5}{G2, G4, G5}{G3, G4, G5}{G1, G2, G3, G4}{G1, G2, G3, G5}{G1, G2, G4, G5}{G1, G3, G4, G5}{G2, G3, G4, G5}{G1, G2, G3, G4, G5}
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Bidding Strategies - Smart-Combination
Bid on all bundles that have 1 or 2 goals
Additionally, bid on the top N bundles containing more than 2 goals.
Given k clusters of s goals (where s is in the set S of cluster sizes >2), N = |S| * max(S) * k.
Goal
Goal Goal
Goal
Goal Goal
Goal
Goal Goal
Goal Goal
Goal
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Bidding Strategies - Nearest-Neighbor
Bid on all "Good Sequences":
* {Gi} for all i
* If S = {Gi, ... Ge} is a good sequence then S U {Gt} is a good sequence if Gt is the closest neighbor to Ge not in S and the value of S U {Gt} ≥ the value of S
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Bidding Strategies - Graph Cut
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Bidding Strategies - Graph Cut
Maximum cuts
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Summary of Experimental Results
Generally Best Performing Bidding Strategies wrt:
Travel Costs -- Graph-Cut
Travel Times -- Three-Combination
Smallest Number of Bids -- Single, then Graph-Cut
Robot Utilization -- Graph-Cut
Important Factors:
Goal distribution (uniform or clustered), number of clusters, prior knowledge of the terrain
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The End
Questions?