characterization of truthful mab mechanisms for multi-slot...
TRANSCRIPT
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Characterization of Truthful MAB Mechanisms forMulti-Slot Sponsored Search Auctions
Sujit Prakash Gujar
Advisor : Y NarahariE-Commerce Lab
Department of Computer Science and AutomationIndian Institute of Science, Bangalore-12
Joint Work with Akash Das SarmaPresented At Xerox Research Center Europe, Grenoble
August 10, 2010
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 1 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Agenda
Introduction to Mechanism Design
Sponsored Search Auctions
Multi-Armed Bandit (MAB) Mechanisms
State of the Art
Research Gaps
Our Contributions and Results
Directions for Future Work
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 2 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Mechanism Design
Game Theory: Analysis of strategic interaction among players
Mechanism Design: Reverse engineering of game theory
Mechanism Design is the art of designing rules of a game to achievea specific outcome in presence of multiple self-interested agents,each with private information about their preferences.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 3 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Mechanism Design
Game Theory: Analysis of strategic interaction among players
Mechanism Design: Reverse engineering of game theory
Mechanism Design is the art of designing rules of a game to achievea specific outcome in presence of multiple self-interested agents,each with private information about their preferences.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 3 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Mechanism Design
Game Theory: Analysis of strategic interaction among players
Mechanism Design: Reverse engineering of game theory
Mechanism Design is the art of designing rules of a game to achievea specific outcome in presence of multiple self-interested agents,each with private information about their preferences.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 3 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 4 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 4 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 4 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 4 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 4 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Incentive Compatibility and Individual Rationality
Individual Rationality
No agent is worse off by participating in the mechanism
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 5 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.
She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.
She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Auctions
First Price Auction (FPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as she has bid for.
Second Price Auction (SPA) for selling a single item.
The bidder with the highest bid wins.She pays as much as the second highest bid.
Vickrey 1 showed : The truth revelation is dominant strategy insecond price auction.
1W. Vickrey. Counter speculation, auctions, and competitive sealed tenders.Journal of Finance, 16(1):8-37, March 1961.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 6 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Mechanism DesignSpace of Mechanisms
Space of Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 7 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Sponsored Search Auctions
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 8 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Sponsored Search Auctions
A Successful Application of Mechanism Design in E-Commerce:Sponsored Search Auctions
Most popular sites: search engines viz. Google, Yahoo!, Bing
Search engines display ads relevant to the search query
Typically limited number of slots for display of such slots
There is an auction running behind the scene for each keyword fordisplay of such ads
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 9 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Challenges in Allocating the slots to the Agents
Billions of dollars
Consider an example
2 agents competing for a single slotAgent 1 bids $1 and Agent 2 bids $0.7
The probability of receiving click on ad for agent 1 is 0.5and agent 2 receives a click if her ad is displayedDisplaying ad of the agent 2 is beneficial for the search engine
The probability of ad receiving a click is referred to asClick-Through-Rate (CTR)
While allocating one should consider the CTRs
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 10 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Challenges in Allocating the slots to the Agents
Billions of dollars
Consider an example
2 agents competing for a single slotAgent 1 bids $1 and Agent 2 bids $0.7The probability of receiving click on ad for agent 1 is 0.5and agent 2 receives a click if her ad is displayedDisplaying ad of the agent 2 is beneficial for the search engine
The probability of ad receiving a click is referred to asClick-Through-Rate (CTR)
While allocating one should consider the CTRs
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 10 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Challenges in Allocating the slots to the Agents
Billions of dollars
Consider an example
2 agents competing for a single slotAgent 1 bids $1 and Agent 2 bids $0.7The probability of receiving click on ad for agent 1 is 0.5and agent 2 receives a click if her ad is displayedDisplaying ad of the agent 2 is beneficial for the search engine
The probability of ad receiving a click is referred to asClick-Through-Rate (CTR)
While allocating one should consider the CTRs
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 10 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Need for Mechanism Design
Agents are strategic
It is critical to know the value that an agent obtains for each clickshe receives, but this is private information
× Popular Mechanisms GFP and GSP are not truthful
Mechanism Design is a natural tool
Design of truthful sponsored search auctions: Aggrawal et. al.2
Design of optimal sponsored search auctions: Garg and Narahari 3
2G. Aggarwal, A. Goel, and R. Motwani. Truthful auctions for pricing searchkeywords. ACM EC’06.
3D. Garg and Y. Narahari. An Optimal Mechanism for Sponsored Search Auctionsand Comparison with other Mechanisms. In, IEEE Transactions on AutomationScience and Engineering, 2009.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 11 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Need for Combining Mechanism Design with MachineLearning
The previous work relied on the knowledge of the CTRs
× Generally neither the search engine nor the advertisers haveknowledge of the CTRs for the ads
Typically the same set of advertisers compete for a particularkeyword
The CTRs can be learnt over the course of repeated auctions
When there is a single slot, the problem is the same as Multi-ArmedBandit (MAB) Problem
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 12 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Multi-Armed Bandit (MAB) Mechanism
Regret: Measure of a performance of a learning algorithm
Regret = Worst case Loss in Social Welfare
One would like to learn CTRs with minimal regret
This calls for combining techniques from Mechanism Design Theoryand Machine Learning
Agents may manipulate the learning algorithm for the underlyingMAB problem
Goal is to design an auction mechanism that is truthful as well aslearns CTRs
Such mechanisms are called as MAB Mechanisms
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 13 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
State of The Art
If agents are not strategic: R(T ) = O(T 1/2)
Nikhil Devanur and Sham M. Kakade, The price of truthfulness forpay-per-click auctions. In Proceedings of the 10th ACM Conferenceon Electronic Commerce, pages 99-106, 2009.
Moshe Babaioff, Yogeshwer Sharma, and Aleksandrs Slivkins,Characterizing Truthful Multi-Armed Bandit Mechanisms, InProceedings of the 10th ACM Conference on Electronic Commerce,pages 79-88, 2009.
Onno Zoeter, On a form of advertiser cheating in sponsored searchand a dynamic-VCG solution. In Proceedings of Workshop onTargeting and Ranking for Online Advertising, TROA, 2008.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 14 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
State of The Art
If agents are not strategic: R(T ) = O(T 1/2)
Nikhil Devanur and Sham M. Kakade, The price of truthfulness forpay-per-click auctions. In Proceedings of the 10th ACM Conferenceon Electronic Commerce, pages 99-106, 2009.
Moshe Babaioff, Yogeshwer Sharma, and Aleksandrs Slivkins,Characterizing Truthful Multi-Armed Bandit Mechanisms, InProceedings of the 10th ACM Conference on Electronic Commerce,pages 79-88, 2009.
Onno Zoeter, On a form of advertiser cheating in sponsored searchand a dynamic-VCG solution. In Proceedings of Workshop onTargeting and Ranking for Online Advertising, TROA, 2008.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 14 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
State of The Art
If agents are not strategic: R(T ) = O(T 1/2)
Nikhil Devanur and Sham M. Kakade, The price of truthfulness forpay-per-click auctions. In Proceedings of the 10th ACM Conferenceon Electronic Commerce, pages 99-106, 2009.
Moshe Babaioff, Yogeshwer Sharma, and Aleksandrs Slivkins,Characterizing Truthful Multi-Armed Bandit Mechanisms, InProceedings of the 10th ACM Conference on Electronic Commerce,pages 79-88, 2009.
Onno Zoeter, On a form of advertiser cheating in sponsored searchand a dynamic-VCG solution. In Proceedings of Workshop onTargeting and Ranking for Online Advertising, TROA, 2008.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 14 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
State of The Art
If agents are not strategic: R(T ) = O(T 1/2)
Nikhil Devanur and Sham M. Kakade, The price of truthfulness forpay-per-click auctions. In Proceedings of the 10th ACM Conferenceon Electronic Commerce, pages 99-106, 2009.
Moshe Babaioff, Yogeshwer Sharma, and Aleksandrs Slivkins,Characterizing Truthful Multi-Armed Bandit Mechanisms, InProceedings of the 10th ACM Conference on Electronic Commerce,pages 79-88, 2009.
Onno Zoeter, On a form of advertiser cheating in sponsored searchand a dynamic-VCG solution. In Proceedings of Workshop onTargeting and Ranking for Online Advertising, TROA, 2008.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 14 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Research Gaps
MAB Mechanisms for sponsored search: Previous work assumes asingle slot
The techniques do not immediately generalize to multi-slot case
The problem that we address
Goal
Characterize truthful Multi-Armed Bandit (MAB) mechanisms for theallocation of advertisers to multiple slots in sponsored search auctionsunder various assumptions on Click-Through Rates (CTRs).
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 15 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Research Gaps
MAB Mechanisms for sponsored search: Previous work assumes asingle slot
The techniques do not immediately generalize to multi-slot case
The problem that we address
Goal
Characterize truthful Multi-Armed Bandit (MAB) mechanisms for theallocation of advertisers to multiple slots in sponsored search auctionsunder various assumptions on Click-Through Rates (CTRs).
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 15 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Research Gaps
MAB Mechanisms for sponsored search: Previous work assumes asingle slot
The techniques do not immediately generalize to multi-slot case
The problem that we address
Goal
Characterize truthful Multi-Armed Bandit (MAB) mechanisms for theallocation of advertisers to multiple slots in sponsored search auctionsunder various assumptions on Click-Through Rates (CTRs).
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 15 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Research Gaps
MAB Mechanisms for sponsored search: Previous work assumes asingle slot
The techniques do not immediately generalize to multi-slot case
The problem that we address
Goal
Characterize truthful Multi-Armed Bandit (MAB) mechanisms for theallocation of advertisers to multiple slots in sponsored search auctionsunder various assumptions on Click-Through Rates (CTRs).
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 15 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Our Contributions
Generalize notion of pointwise monotonicity: Strong Monotonicityand Weak Monotonicity
Introduce notion of Type-I Separatedness and Type-IISeparatedness
Characterization of truthful MAB mechanisms for unknown andunconstrained CTRs
Necessary conditions for a MAB mechanism to be truthful withvarious assumptions on CTRs
Sufficient conditions for a MAB mechanism to be truthful withvarious assumptions on CTRs
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 16 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Notation
m Number of slots
i Index of an agent, i = 1, 2, . . . , k
j Index of a slot, j = 1, 2, . . . , m
T Total number of rounds
t A particular round. t ∈ 1, 2, . . . , TAij(t) = 1 if an agent i is allocated slot j in round t
= 0 otherwiseA(t) (Aij(t))i∈K ,j∈M
A = (A(1), A(2), . . . , A(T )), Allocation rule
ρij(t) = 1 if agent i gets a click in slot j in round t= 0 otherwise
ρ(t) (ρij(t))i∈K ,j∈M
ρ = (ρ(1), ρ(2), . . . , ρ(T ))
vi Agent i ’s valuation of a click to her ad
bi Bid by agent i
b Bid vector, indicating bids of all the agents= (bi , b−i ) = (b1, b2, . . . , bk)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 17 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Ci (b, ρ) Total number of clicks obtained by an agent iin T rounds
Pi (b, ρ) Payment made by agent i
P(b, ρ) = (P1(. ), P2(. ), . . . , Pk(. )), Payment rule
Ui (vi , b, ρ) Utility of an agent i in T rounds= viCi (b, ρ)− Pi (b, ρ)
b+i A real number > bi
αi Click probability associated with agent i
βj Click probability associated with slot j
µij The probability that an ad of an agent i receivesclick when the agent is allotted slot j .
N(b, ρ, i , t) Set of slot agent pairs in round tthat influence agent i in some future rounds
Table: Notation
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 18 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Myerson4 designed an optimal auction for the seller.
He characterized the truthful mechanisms
Technique developed by him applies to most single parameterdomains
Myerson Characterization: Let (A,P) be a normalized mechanismfor the MAB mechanism design problem. It is truthful withunrestricted payment computation if and only if for any givenrealization ρ the corresponding click-allocation C is non-decreasingand the payment rule is given by,
Pi (bi , b−i ; ρ) = bi · Ci (x , b−i ; ρ)−∫ bi
0
Ci (x , b−i ; ρ)dx
4R. B. Myerson. Optimal auction design. Math. Operations Res., 6(1):58-73, Feb.1981.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 19 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Characterization of Truthful MAB mechanism for singleslot case
Babaioff5 et. al. showed,
Theorem
Consider the MAB mechanism design problem. Let A be anon-degenerate, deterministic allocation rule. Then mechanism (A,P) isnormalized and truthful for some payment rule P if and only if A ispointwise monotone and weakly separated.
5M. Babaioff, Y. Sharma, and A. Slivkins. Characterizing truthful multi-armedbandit mechanisms. ACM EC’09
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 20 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Allocation Rule Properties
Normalized: Payment is non negative and no agent pays more thanwhat she has bid for. That is,
∀ i ,∀ b, ρ, Pi (·) ≥ 0 and Pi (·) ≤ bi · Ci (·)
Non-degenerate: For any agent at each bid, small perturbation inbid does not affect her allocation. That is, ∀ i ,∀ bi ∀b−i , ρ, ∃ I 3 bi such that,
Ai (x , b−i ; ρ) = Ai (bi , b−i ; ρ) ∀x ∈ I
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 21 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Monotonicity
Definition (Strong Pointwise Monotonicity)
An allocation rule is said to be strongly pointwise monotone if it satisfies:For any fixed (b−i , ρ), if an agent i with bid bi is allocated a slot j inround t, then ∀ b+
i > bi , she is allocated the same slot j in round t.
Higher bid: agent receives the same slot in round t,Lower bid:, she may receive the same slot or may lose the impression.
Definition (Weak Pointwise Monotonicity)
We call an allocation rule weak pointwise monotone if, for any given(b−i , ρ), and bid b+
i > bi , Aij((bi , b−i ), ρ, t) = 1 ⇒Aij′((b
+i , b−i ), ρ, t) = 1 for some slot j ′ ≤ j , ∀t.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 22 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Monotonicity
Definition (Strong Pointwise Monotonicity)
An allocation rule is said to be strongly pointwise monotone if it satisfies:For any fixed (b−i , ρ), if an agent i with bid bi is allocated a slot j inround t, then ∀ b+
i > bi , she is allocated the same slot j in round t.
Higher bid: agent receives the same slot in round t,Lower bid:, she may receive the same slot or may lose the impression.
Definition (Weak Pointwise Monotonicity)
We call an allocation rule weak pointwise monotone if, for any given(b−i , ρ), and bid b+
i > bi , Aij((bi , b−i ), ρ, t) = 1 ⇒Aij′((b
+i , b−i ), ρ, t) = 1 for some slot j ′ ≤ j , ∀t.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 22 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Example
Consider, k = 4 agents, m = 2 slots, T = 1000 rounds
CTRs, µij decreasing for each agent i
Let an allocation A be:
For the first 100 rounds, advertisements of four agents displayed inround robin fashionFor the remaining 900 rounds, the advertisements are displayed thatmaximize the expected sum of valuations of the clicks
A described here is weakly pointwise monotone
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 23 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
More Definitions
Definition (Influential Set)
Given a bid vector, b, a realization ρ and round t, an influential setI (b, ρ, t) is the set of all agent-slot allocation pairs (i , j), such that (i)Aij(b, ρ, t) = 1 and (ii) a change in ρij(t) will result in a change in theallocation in a future round. t is referred to as an influential round.Agent i is referred to as an influential agent and j as influential slot w.r.tround t.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 24 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Separatedness
Definition (Type-I Separated)
We call an allocation rule Type-I separated if for a given (b−i , ρ), ifN((bi , b−i ), ρ, i , t) is an i-influential set, then∀ (i ′, j ′) ∈ N((bi , b−i ), ρ, i , t), Ai ′j′ = 1 when the agent i increases herbid to b+
i .
When an agent i increases her bid, while the other parameters are keptfixed, the allocation in the originally influential slots does not change,though the influentiality of that agent-slot pair may be lost.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 25 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Definition (Type-II Separated)
We call an allocation rule Type-II separated if for a given (b−i , ρ) and twobids of agent i , bi and b+
i > bi , N((bi , b−i ), ρ, i , t) ⊆ N((b+i , b−i ), ρ, i , t).
This means that when an agent i increases her bid, while the otherparameters are kept fixed, the allocation in the originally influential slotsdoes not change and they remain influential.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 26 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Example
Consider, k = 4 agents, m = 2 slots, T = 2 rounds
Let an allocation A be:
First round, the ad of the agent i is displayed in the slot i , i = 1, 2.If any ad receives click, same ad is retained in same slotIf the ad in slot i is not clicked
i If bi < bi+2, in round 2, the ad of the agent i + 2 is displayed in slot iii Else, the original ad is retained
A described here is Type-I separated
A described here is not Type-II separated (If b1 > b3, agent 1 is notinfluential for herself)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 27 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Our Results
Number of Learning Parameter Solution Allocation rule Worst CaseSlots (m) (CTR) Concept Characterization Regret
m = 1 Unrestricted DSIC Pointwise monotone & Θ(T 2/3)Exploration separated
m ≥ 1 Unrestricted DSIC Strongly pointwise Θ(T )monotone andType-I separated
m ≥ 1 Higher Slot Click DSIC Weakly pointwise monotone & regret analysisPrecedence Type-I separated open
(Necessary Condition)m ≥ 1 CTR Pre-estimates Truthful in Weakly Pointwise monotone & regret analysis
available expectation Type-I separated (Necessary) openType-II Separated (Sufficient)
m ≥ 1 Separable CTR Truthful in Weakly Pointwise monotone & Ω(T 2/3)expectation Type-I separated (Necessary) (Experimental
Type-II Separated (Sufficient) Evidence)
Table: Results
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 28 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Theorem
Theorem
Let (A,P) be a deterministic, non-degenerate mechanism for the MAB,multi-slot sponsored search auction, with unconstrained and unknown µij .Then, mechanism (A,P) is DSIC iff A is strongly pointwise monotoneand Type-I separated. Further, the payment scheme is given by,
Pi ((bi , b−i ), ρ) = biCi ((bi , b−i ), ρ)−∫ bi
0
Ci ((x , b−i ), ρ)dx .
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 29 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Sketch of the Proof
Monotonic Allocation - # clicks should increase with her bid
For the unknown and unconstrained CTRs this leads to a need ofstrong pointwise monotonicity
Payment should be in the form as given by Theorem 1This can be derived from Myerson Characterization
Payment should be computable from the observed clicks: Type -Iseparatedness is necessary
Type-I separatedness along with the strong pointwise monotonicity issufficient for truthful implementation
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 30 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Implications of Strong Monotonicity
In a particular round, for a fixed game instance, if an agent isallocated a particular slot, she has to be allocated same slot at allhigher bids
This is a very strong necessity
It leads to instances on which regret is O(T )
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 31 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Implications of Strong Monotonicity
In a particular round, for a fixed game instance, if an agent isallocated a particular slot, she has to be allocated same slot at allhigher bids
This is a very strong necessity
It leads to instances on which regret is O(T )
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 31 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Implications of Strong Monotonicity
In a particular round, for a fixed game instance, if an agent isallocated a particular slot, she has to be allocated same slot at allhigher bids
This is a very strong necessity
It leads to instances on which regret is O(T )
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 31 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
What Next?
Three escape routes
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 32 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Higher Order Click Precedence
Assume, if there is a click on ad in slot j , then all previous slots receiveclick.
Proposition
Consider the setting in which realization ρ follows Higher Slot ClickPrecedence. Let (A,P) be a deterministic non-degenerate DSICmechanism for this setting. Then the allocation rule A must be weakpointwise monotone and Type-I separated. Further, the payment schemeis given by,
Pi (bi , b−i ; ρ) = biCi (bi , b−i ; ρ)−∫ bi
0
Ci (x , b−i ; ρ)dx
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 33 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Higher Order Click Precedence
Assume, if there is a click on ad in slot j , then all previous slots receiveclick.
Proposition
Consider the setting in which realization ρ follows Higher Slot ClickPrecedence. Let (A,P) be a deterministic non-degenerate DSICmechanism for this setting. Then the allocation rule A must be weakpointwise monotone and Type-I separated. Further, the payment schemeis given by,
Pi (bi , b−i ; ρ) = biCi (bi , b−i ; ρ)−∫ bi
0
Ci (x , b−i ; ρ)dx
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 33 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Truthful In Expectation
Definition (Truthful in Expectation)
A mechanism is said to be truthful in expectation over µ, the CTRpre-estimate, if each of the agents believes that the number of clicks sheobtains is indeed
∑t
∑j(µijAij(·)), which is the number of clicks she will
obtain if the CTR pre-estimate is perfectly accurate.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 34 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
CTR Pre-estimates are Available
Theorem
Let (A,P) be a mechanism for this stochastic multi-round auction settingwhere A is a non-degenerate, deterministic and fair allocation rule. Then,(A,P) is truthful in expectation over µ if A is weakly pointwise monotoneand Type-II separated and the payment scheme is given by,
Pi (b, ρ) =T∑
t=1
m∑j=1
µijbiAij(b, ρ, t)−∫ bi
0
Aij(x , b−i , ρ, t)dx
Also, if a mechanism (A,P) is truthful, then it is weakly pointwisemonotone, Type-I separated, the payment is given as above and iscomputable.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 35 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Sponsored Search AuctionsState-of-the-ArtResearch GapsOur Approach
Separable CTRs
Theorem
Let (A,P) be a mechanism for the stochastic multi-round auction settingwhere A is a non-degenerate, deterministic and fair allocation rule. Then,(A,P) is truthful in expectation over µ′ if A is weakly pointwisemonotone and Type-II separated and the payment scheme is given by,
Pi (b, ρ) =T∑
t=1
m∑j=1
µ′ijbiAij(b, ρ, t)−∫ bi
0
Aij(x , b−i , ρ, t)dx
Also, if a mechanism (A,P) is truthful, then it is weakly pointwisemonotone, Type-I separated, the payment is given as above, and iscomputable.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 36 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Our Results
Number of Learning Parameter Solution Allocation rule Worst CaseSlots (m) (CTR) Concept Characterization Regret
m = 1 [2] Unrestricted DSIC Pointwise monotone & Θ(T 2/3)Exploration separated
m ≥ 1 Unrestricted DSIC Strongly pointwise Θ(T )monotone andType-I separated
m ≥ 1 Higher Slot Click DSIC Weakly pointwise monotone & regret analysisPrecedence Type-I separated open
(Necessary Condition)m ≥ 1 CTR Pre-estimates Truthful in Weakly Pointwise monotone & regret analysis
available expectation Type-I separated (Necessary) openType-II Separated (Sufficient)
m ≥ 1 Separable CTR Truthful in Weakly Pointwise monotone & Ω(T 2/3)expectation Type-I separated (Necessary) (Experimental
Type-II Separated (Sufficient) Evidence)
Table: Results
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 37 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Summary
We have seen,
Characterization of truthful mechanisms with Unknown andUnconstrained CTRs
Need of a strong monotonicity puts severe restrictions on truthfulallocation rules
How the relation across the CTRs can be exploited
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 38 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Summary
We have seen,
Characterization of truthful mechanisms with Unknown andUnconstrained CTRs
Need of a strong monotonicity puts severe restrictions on truthfulallocation rules
How the relation across the CTRs can be exploited
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 38 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Summary
We have seen,
Characterization of truthful mechanisms with Unknown andUnconstrained CTRs
Need of a strong monotonicity puts severe restrictions on truthfulallocation rules
How the relation across the CTRs can be exploited
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 38 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,
1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,
1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,
1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)
2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Direction for future work
Fill in the gaps in necessary and sufficient conditions
Regret analysis
Weaker solution concepts,1 Approximate ex-post Nash Incentive Compatibility (Parkes et al)2 Bayesian Incentive Compatibility
Randomized mechanisms6
6M. Babaioff, R Kleinberg, and A Slivkins, Truthful Mechanisms with ImplicitPayment Computation, in ACM Conference on Electronic Commerce (EC’10)
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 39 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Literature Review
For Sponsored Search Auctions: [3, 4, 5]Web Information: http://advertising.yahoo.com/,http://adwords.google.com
For Mechanism Design: [5, 6, 7]
Multi-Armed Bandit Problems: [8, 9]
MAB Mechanisms for sponsored search: [10, 2, 11, 12, 13]
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 40 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
R. B. Myerson.Optimal auction design.Math. Operations Res., 6(1):58–73, Feb. 1981.
M. Babaioff, Y. Sharma, and A. Slivkins.Characterizing truthful multi-armed bandit mechanisms: extendedabstract.In Proceedings of the 10th ACM Conference on ElectronicCommerce, pages 79–88, Stanford, California, 2009.
G. Aggarwal, A. Goel, and R. Motwani.Truthful auctions for pricing search keywords.In EC ’06: Proceedings of the 7th ACM conference on Electroniccommerce, pages 1–7, New York, NY, USA, 2006.
B. Edelman, M. Ostrovsky, and M. Schwarz.Internet advertising and the generalized second price auction: Sellingbillions of dollars worth of keywords.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 40 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
In 2nd Workshop on Sponsored Search Auctions in conjunction withthe ACM Conference on Electronic Commerce (EC’06), Ann Arbor,MI, June 2006.
Y. Narahari, D. Garg, N. Rama Suri, and H. Prakash.Game Theoretic Problems in Network Economics and MechanismDesign Solutions.Advanced Information and Knowledge Processing Series, Springer,London, 2009.
Dinesh Garg, Y Narahari, and Sujit Gujar.Foundations of mechanism design: A tutorial - part 1: Key conceptsand classical results.Sadhana - Indian Academy Proceedings in Engineering Sciences,33(Part 2):83–130, April 2008.
Dinesh Garg, Y Narahari, and Sujit Gujar.Foundations of mechanism design: A tutorial - part 2: Advancedconcepts and results.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 40 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Sadhana - Indian Academy Proceedings in Engineering Sciences,33(Part 2):131–174, April 2008.
H. Robbins.Some aspects of the sequential design of experiments.Bulletin of American Maths Society, 58, Number 5:527–535, 1952.
P. Auer, N. Cesa-Bianchi, and P. Fischer.Finite-time analysis of the multiarmed bandit problem.Machine Learning, 47(2-3):235–256, 2002.
N. R. Devanur and S. M. Kakade.The price of truthfulness for pay-per-click auctions.In Proceedings of the 10th ACM Conference on ElectronicCommerce, pages 99–106, 2009.
R. Gonen and E. Pavlov.An adaptive sponsored search mechanism delta -gain truthful invaluation, time, and budget.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 40 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
In Third International Workshop on Internet and NetworkEconomics, WINE07,, volume 4858 of Lecture Notes in ComputerScience, pages 341–346. Springer, 2007.
R. Gonen and E. Pavlov.An incentive-compatible multi-armed bandit mechanism.In Proceedings of Principles of Distributed Computing, PODC ’07,pages 362–363, New York, NY, USA, 2007. ACM.
Akash Das Sarma, Sujit Gujar, and Y. Narahari.Multi-armed bandit mechanisms for multi-slot sponsored searchauctions.CoRR, abs/1001.1414, 2010.Working Paper, Dept of CSA, Indian Institute of Science, Bangalore.
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 41 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Questions?
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 41 / 42
IntroductionSponsored Search Auctions and MAB Mechanisms
Conclusion
Our ResultsSummaryReferences
Thank You!!!
Sujit Prakash Gujar (CSA, IISc) Truthful MAB Mechanisms August 10, 2010 42 / 42