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# Robot Exploration with Combinatorial Auctions

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### Robot Exploration with Combinatorial Auctions

1. 1. http://www.sciencedaily.com/releases/2007/06/070609112916.htm
2. 2. Robot Exploration with Combinatorial Auctions M. 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
3. 3. Optimal Task Allocation Repeat Auctions + Combinatorial Auctions + Bidding Strategy = Near Optimal Allocation http://shirt.woot.com/Derby/Entry.aspx?id=30206
4. 4. Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
5. 5. Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
6. 6. Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
7. 7. Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
8. 8. Single Item vs. Combinatorial Auctions
9. 9. Single Item vs. Combinatorial Auctions Possible 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}
10. 10. 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})
11. 11. Task Synergies - Negative Travel Distance for R1: T(S) T({G3}) = 4 T({G1}) = 8 T({G3, G1}) = 16 T({G3, G1}) ≥ T({G3}) + T({G1})
12. 12. 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/
13. 13. Bidding Strategies - Single Same as single item auction
14. 14. Bidding Strategies - Three-Combination Possible 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}
15. 15. 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
16. 16. Bidding Strategies - Nearest-Neighbor Bid on all &quot;Good Sequences&quot;: * {G i } for all i * If S = {G i , ... G e } is a good sequence then S U {G t } is a good sequence if G t is the closest neighbor to G e not in S and the value of S U {G t } ≥ the value of S
17. 17. Bidding Strategies - Graph Cut
18. 18. Bidding Strategies - Graph Cut Maximum cuts
19. 19. 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 Smallest Robot Utilization -- Graph-Cut Important Factors: Goal distribution (uniform or clustered), number of clusters, prior knowledge of the terrain
20. 20. Other Notes When targets are uniformly distributed, all bidding strategies are fairly close wrt travel costs. Nearest-Neighbor and Graph-Cut tend to have large bundle sizes => smaller number of active robots Smaller robot utilization => smaller travel costs, but larger travel times
21. 21. The End Questions?