google’s adwords market: how theory influenced practice · nmaximize google’s revenue...
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Google’s AdWords Market:How Theory Influenced Practice
Vijay V. Vazirani
University of California, Irvine
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Two major achievements of Google
1). Search: That is robust to spam
2). Advertising: Business model
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Revolution in advertising
n Matching merchants with customers¨ How can a merchant pitch ads in a targeted way
to customers who are interested in his goods.
n Difficulty: How to find out needs/desires of customers in a super-efficient manner?
n Insight: A user’s search queries reveals to Google a succinct window into her mind/needs
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n Solution: Auction off queried keywords to advertisers!
n This converts a giant undefined matching problem into a gigantic auction!
n Google is world’s biggest auction house: billions daily!
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How to allocate keywords to advertisers?
n Advertisers bid for specific keywordsn Maximize Google’s revenue – efficient solution!
n GREEDY: Display the ad of highest bidder ¨ Assume: only 1 ad is shown
n Charge bid, or second highest bid (Vickery auction)
This soln. was being used!
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Problem …
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Example:
$1 $0.99
$1 $0
Book
CD
Bidder1 Bidder 2
B1 = B2 = $100
Queries: 100 Books then 100 CDs
Bidder 1 Bidder 2
Algorithm Greedy
LOSTRevenue$100
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Example:
$1 $0.99
$1 $0
Book
CD
Bidder1 Bidder 2
B1 = B2 = $100
Queries: 100 Books then 100 CDs
Bidder 1 Bidder 2
Optimal Allocation
Revenue$199
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Must incorporate budgets in solution
n Large fraction of advertisers are budget-constrained
n Budget distribution is heavy-tailed
Must handle small budget advertisers adequately
n Solution must be real time and particularly simple!
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Adwords Problem
Mehta, Saberi, Vazirani & V, 2005:
Simple framework that captures essential features.
Will add bells and whistles later!
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The Adwords Problem
N advertisers. ¨ Daily Budgets B1, B2, …, BN = $1¨ Each advertiser provides bids for keywords he is interested in.
Search EngineSelect one Ad
Advertiser pays his bid
queries (online)
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Online competitive analysis
n Compare revenue of online algorithm with that of best offline allocation.
n E.g., GREEDY has competitive ratio of ½.
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Algorithm
n Will use agents’ ¨Bid ¨Fraction of budget spent
n “Correct” tradeoff between them given by a special function f
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Algorithm
Award next query to bidder with max bid (fraction of budget spent)×"
" # = 1 − '((*(+)
1 − 1/' competitive ratio, assuming bid << budget Optimal! Simple, minimalistic solution!
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Impact
n Provided a general framework for thinking about budget constrained auctions for many Ad products
n Bid scaling used widely in industry for ad auctions and for display ads:¨ Very fast: one operation per bid¨ Low on memory: one number per bid¨ No extra communication
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New algorithmic work
n Numerous models: ¨Queries arrive in random order¨Queries are picked from a distribution¨Submodular constraints on allocations¨Use historical data about query arrival¨ . . .
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Solution has roots in “pure” theory,in particular, Matching Theory!
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Online bipartite matching
!
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Online bipartite matching
! "
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Online bipartite matching
! "
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Online bipartite matching
! "
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Online bipartite matching
! "
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Online bipartite matching
! "
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n Any deterministic algorithm has competitive ratio of 1/2.
n Karp, Vazirani & V., 1990:1 − 1/$ factor randomized algorithm
Optimal!
n Same as simple case of Adwords problem:All budgets $1, all bids $0/1.
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Online !-matching
n Kalyanasundaram & Pruhs, 1996:1 − 1/% factor algorithm for b-matching:Daily budgets $!, bids $0/1, b>>1
BALANCE: Assign query to interested bidder who has spent least so far.
Optimal!
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Example: Balance
$1 $1
$1 $0
Book
CD
Bidder1 Bidder 2
B1 = B2 = $100
Queries: 100 Books then 100 CDs
Bidder 1 Bidder 2
Balance Algorithm
Revenue$1.50
¾-competitive
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Where did this tradeoff function come from?
New Proof forBALANCE {0,1}
Factor Revealing LP
Modify LP for arbitrary bids [0,1]
Use dual to get Tradeoff function
Tradeoff Revealing LP
1-1/e
1-1/e
(Jain, Mahdian, Markakis, Saberi & V., ’03)
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New proof of BALANCE
n N bidders, $1 each. Each bid is $!.
n OPT: optimal offline, ALG: BALANCE
n OPT = N
n Will show: ALG ≥ $ 1 − '(
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n Idea: Upper bound no. of bidders who spent less!
n Assume k large
n !": Bidders who spent #"$%& , ("&
n Let |!"| = *". Will constrain *%, *% + *,, …
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!"!#
ALG
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n Partition revenue of ALG
n $" ∈ $%&'( ) if bidder had *+,-. , 0+.when this money was spent.
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!"!#
ALGLayer 2Layer 1
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n Partition revenue of ALG
n $" ∈ $%&'( ) if bidder had *+,-. , 0+.when this money was spent.
n BALANCE assigns next query to interested bidder who has spent least so far.
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The picture can't be displayed.
•First Constraint: !" = $" ≤ &'()* 1 ≤ ,-
Layer 1 ≤ ,-
!"
Layer1
OPT
q
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Second Constraint: !" ∪ !$ = &" + &$ ≤ () +
(+,-)
Layer 2 ≤ (+,-)
Layer 2+
Layer 1!"!$
OPT
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Lower bound on ALG
LP(N): min ∑" "# $"s.t. constraints on $%, $' , … $#
ALG ≥ * 1 − 1 − %##
≥ * 1 − %-
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Factor revealing LP
n Jain, Mahdian, Markakis, Saberi & V., ’03
n Family of LPs: LP(N) encodes problem of finding lower bound for instance of size !.
n Infimum of optimal solutions gives approximation factor
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Where did this tradeoff function come from?
New Proof forBALANCE {0,1}
Factor Revealing LP
Modify LP for arbitrary bids [0,1]
Use dual to get Tradeoff function
Tradeoff Revealing LP
1-1/e
1-1/e
(Jain, Mahdian, Markakis, Saberi & V., ’03)
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Larger Theme
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AdWords, Amazon, eBay, Yahoo!, Alibaba, Uber,Apple (iTunes), Airbnb,
Cloud Computing …
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Markets on the Internet
n Numerous new algorithmic and game-theoretic issues raised.
n Much scope for creative work that can have a huge impact!