大数据挖掘advertising

1、CS 345Data MiningOnline algorithmsSearch advertising共三十七页Online algorithmsClassic model of algorithmsYou get to see the entire input, then compute some function of itIn this context, “offline algorithm”Online algorithmYou get to see the input one piece at a time, and need to make irrevocable decisio

2、ns along the waySimilar to data stream models共三十七页Example: Bipartite matching1234abcdGirlsBoys共三十七页Example: Bipartite matching1234abcdM = (1,a),(2,b),(3,d) is a matchingCardinality of matching = |M| = 3GirlsBoys共三十七页Example: Bipartite matching1234abcdGirlsBoysM = (1,c),(2,b),(3,d),(4,a) is a perfect

3、 matching共三十七页Matching AlgorithmProblem: Find a maximum-cardinality matching for a given bipartite graphA perfect one if it existsThere is a polynomial-time offline algorithm (Hopcroft and Karp 1973)But what if we dont have the entire graph upfront?共三十七页Online problemInitially, we are given the set

4、BoysIn each round, one girls choices are revealedAt that time, we have to decide to either:Pair the girl with a boyDont pair the girl with any boyExample of application: assigning tasks to servers共三十七页Online problem1234abcd(1,a)(2,b)(3,d)共三十七页Greedy algorithmPair the new girl with any eligible boyIf

5、 there is none, dont pair girlHow good is the algorithm?共三十七页Competitive RatioFor input I, suppose greedy produces matching Mgreedy while an optimal matching is MoptCompetitive ratio = minall possible inputs I (|Mgreedy|/|Mopt|)共三十七页Analyzing the greedy algorithmConsider the set G of girls matched i

6、n Mopt but not in MgreedyThen it must be the case that every boy adjacent to girls in G is already matched in MgreedyThere must be at least |G| such boysOtherwise the optimal algorithm could not have matched all the G girlsTherefore |Mgreedy| |G| = |Mopt - Mgreedy|Mgreedy|/|Mopt| 1/2共三十七页Worst-case

7、scenario1234abc(1,a)(2,b)d共三十七页History of web advertisingBanner ads (1995-2001)Initial form of web advertisingPopular websites charged X$ for every 1000 “impressions” of adCalled “CPM” rateModeled similar to TV, magazine adsUntargeted to demographically tagetedLow clickthrough rateslow ROI for adver

8、tisers共三十七页Performance-based advertisingIntroduced by Overture around 2000Advertisers “bid” on search keywordsWhen someone searches for that keyword, the highest bidders ad is shownAdvertiser is charged only if the ad is clicked onSimilar model adopted by Google with some changes around 2002Called “

9、Adwords”共三十七页Ads vs. search results共三十七页Web 2.0Performance-based advertising works!Multi-billion-dollar industryInteresting problemsWhat ads to show for a search?If Im an advertiser, which search terms should I bid on and how much to bid?共三十七页Adwords problemA stream of queries arrives at the search

10、engineq1, q2,Several advertisers bid on each queryWhen query qi arrives, search engine must pick a subset of advertisers whose ads are shownGoal: maximize search engines revenuesClearly we need an online algorithm!共三十七页Greedy algorithmSimplest algorithm is greedyIts easy to see that the greedy algor

11、ithm is actually optimal!共三十七页Complications (1)Each ad has a different likelihood of being clickedAdvertiser 1 bids $2, click probability = 0.1Advertiser 2 bids $1, click probability = 0.5Clickthrough rate measured historicallySimple solutionInstead of raw bids, use the “expected revenue per click”共

12、三十七页The Adwords InnovationAdvertiserBidCTRBid * CTRABC$1.00$0.75$0.501%2%2.5%1 cent1.5 cents1.125 cents共三十七页The Adwords InnovationAdvertiserBidCTRBid * CTRABC$1.00$0.75$0.501%2%2.5%1 cent1.5 cents1.125 cents共三十七页Complications (2)Each advertiser has a limited budgetSearch engine guarantees that the a

13、dvertiser will not be charged more than their daily budget共三十七页Simplified model (for now)Assume all bids are 0 or 1Each advertiser has the same budget BOne advertiser per queryLets try the greedy algorithmArbitrarily pick an eligible advertiser for each keyword共三十七页Bad scenario for greedyTwo adverti

14、sers A and BA bids on query x, B bids on x and yBoth have budgets of $4Query stream: xxxxyyyyWorst case greedy choice: BBBB_Optimal: AAAABBBBCompetitive ratio = Simple analysis shows this is the worst case共三十七页BALANCE algorithm MSVVMehta, Saberi, Vazirani, and VaziraniFor each query, pick the advert

15、iser with the largest unspent budgetBreak ties arbitrarily共三十七页Example: BALANCETwo advertisers A and BA bids on query x, B bids on x and yBoth have budgets of $4Query stream: xxxxyyyyBALANCE choice: ABABBB_Optimal: AAAABBBBCompetitive ratio = 共三十七页Analyzing BALANCEConsider simple case: two advertise

16、rs, A1 and A2, each with budget B (assume B 1)Assume optimal solution exhausts both advertisers budgetsBALANCE must exhaust at least one advertisers budgetIf not, we can allocate more queriesAssume BALANCE exhausts A2s budget共三十七页Analyzing BalanceA1A2BxyBA1A2xOpt revenue = 2BBalance revenue = 2B-x =

17、 B+yWe have y xBalance revenue is minimum for x=y=B/2Minimum Balance revenue = 3B/2Competitive Ratio = 3/4Queries allocated to A1 in optimal solutionQueries allocated to A2 in optimal solution共三十七页General ResultIn the general case, worst competitive ratio of BALANCE is 11/e = approx. 0.63Interesting

18、ly, no online algorithm has a better competitive ratioWont go through the details here, but lets see the worst case that gives this ratio共三十七页Worst case for BALANCEN advertisers, each with budget B N 1NB queries appear in N rounds of B queries eachRound 1 queries: bidders A1, A2, , ANRound 2 queries

19、: bidders A2, A3, , ANRound i queries: bidders Ai, , ANOptimum allocation: allocate round i queries to AiOptimum revenue NB共三十七页BALANCE allocationA1A2A3AN-1ANB/NB/(N-1)B/(N-2)After k rounds, sum of allocations to each of bins Ak,AN is Sk = Sk+1 = = SN = 1 1 kB/(N-i+1)If we find the smallest k such t

20、hat Sk B, then after k roundswe cannot allocate any queries to any advertiser共三十七页BALANCE analysisB/1 B/2 B/3 B/(N-k+1) B/(N-1) B/NS1S2Sk = B 1/1 1/2 1/3 1/(N-k+1) 1/(N-1) 1/NS1S2Sk = 1 共三十七页BALANCE analysisFact: Hn = 1 i n1/i = approx. log(n) for large nResult due to Euler1/1 1/2 1/3 1/(N-k+1) 1/(N-1) 1/NSk = 1 log(N)log(N)-1Sk = 1 implies HN-k = log(N)-1 = log(N/e)N-k = N/ek = N(1-1/e)共三十七页BALANCE analysisSo after the first N(1-1/e) rounds, we cannot allocate a query to any advertiserRevenue = BN(1-1/e)Competitive ratio = 1-1/e共三十七页General versi