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http://www.sciencedaily.com/releases/2007/06/070609112916.htm
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
Optimal Task Allocation
Repeat Auctions
+
Combinatorial Auctions
+
Bidding Strategy
=
Near Optimal Allocation
http://shirt.woot.com/Derby/Entry.aspx?id=30206
Repeat Auctions
Robot1
Robot2
Goal
UnknownTerrain
Wall
Repeat Auctions
Robot1
Robot2
Goal
UnknownTerrain
Wall
Repeat Auctions
Robot1
Robot2
Goal
Wall
Wall
Repeat Auctions
Robot1
Robot2
Goal
Wall
Wall
Single Item vs. Combinatorial Auctions
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}
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})
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})
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/
Bidding Strategies - Single
Same as single item auction
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}
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
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
Bidding Strategies - Graph Cut
Bidding Strategies - Graph Cut
Maximum cuts
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
The End
Questions?