online ad serving: theory and practice - sigmetrics

Online Ad Serving: Theory and Practice

Aranyak MehtaVahab Mirrokni

June 7, 2011

Outline of this talk

I Ad delivery for contract-based settingsI Ad ServingI Planning

I Ad serving in repeated auction settingsI General architecture.I Allocation for budget constrained advertisers.

I Other interactionsI Learning + allocationI Learning + auctionI Auction + contracts

Contract-based Ad Delivery: Outline

I Basic InformationI Ad Serving.

I Targeting.I Online Allocation

I Ad Planning: Reservation

Contract-based Online Advertising

I Pageviews (impressions) instead of queries.

I Display/Banner Ads, Video Ads, Mobile Ads.

I Cost-Per-Impression (CPM).

I Not Auction-based: offline negotiations + Online allocations.

Display/Banner Ads:

I Q1, 2010: One Trillion Display Ads in US. $2.7 billion.

I Top Advertiser: AT&T, Verizon, Scottrade.

I Ad Serving Systems e.g. Facebook, Google Doubleclick,AdMob.

Display/Banner Ads:

Internet Advertising Revenues - 2010

Search

Display

Classified

Internet Ad Revenues - 2010

24% increase

Total $26.0 billion

Display Ad Delivery: Overview

Planning:

Display Ad Delivery

Ad Serving: Targeting: Allocation:

1. Planning: Contracts/Commitments with Advertisers.2. Ad Serving:

I Targeting: Predicting value of impressions.I Ad Allocation: Assigning Impressions to Ads Online.

I Objective Functions:I Efficiency: Users and Advertisers. Revenue of the Publisher.I Smoothness, Fairness, Delivery Penalty.

Planning:

Display Ad Delivery

Strategic, Stochastic

Online, Stochastic

Offline, Online

Planning:

Display Ad Delivery

Online, Stochastic

Offline, Online Forecasting

Demand for ads

Supply of impressions

Planning:

Display Ad Delivery

Delivery Constraints, Budget

Online, Stochastic

Demand for ads

Planning:

Display Ad Delivery

Online, Stochastic

Demand for ads

Planning:

Display Ad Delivery

Online, Stochastic

Demand for ads

I Targeting.I Online Ad Allocation

Targeting

Estimating Value of an impression.

I Behavioral TargetingI Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can

Behavioral Targeting Help Online Advertising?

I Contextual TargetingI Information Retrieval (IR).I Broder, Fontoura, Josifovski, Riedel, A semantic approach to

contextual advertising

I Creative OptimizationI Experimentation

Targeting

Estimating Value of an impression.I Behavioral Targeting

I Interest-based Advertising.I Yan, Liu, Wang, Zhang, Jiang, Chen, 2009, How much can

Targeting

Predicting value of Impressions for Display Ads

I Estimating Click-Through-Rate (CTR).I Budgeted Multi-armed Bandit

I Probability of Conversion.

I Long-term vs. Short-term value of display ads?I Archak, Mirrokni, Muthukrishnan, 2010 Graph-based Models.

I Computing Adfactors based on AdGraphsI Markov Models for Advertiser-specific User Behavior

Predicting value of Impressions for Display Ads

I Estimating Click-Through-Rate (CTR).I Budgeted Multi-armed Bandit

I Probability of Conversion.I Long-term vs. Short-term value of display ads?

I Archak, Mirrokni, Muthukrishnan, 2010 Graph-based Models.I Computing Adfactors based on AdGraphsI Markov Models for Advertiser-specific User Behavior

I Basic Information

I Ad Planning: ReservationI Ad Serving.

I Targeting.I Online Ad Allocation

Outline: Online Allocation

I Online Stochastic Assignment ProblemsI Online (Stochastic) MatchingI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental Results

I Online Learning and Allocation

Online Ad Allocation

I When page arrives, assign an eligible ad.I value of assigning page i to ad a: via

I Display Ads (DA) problem:I Maximize value of ads served: max

∑i,a viaxia

I Capacity of ad a:∑

i∈A(a) xia ≤ Ca

I When page arrives, assign an eligible ad.I value of assigning page i to ad a: via

I Display Ads (DA) problem:I Maximize value of ads served: max

∑i,a viaxia

I Capacity of ad a:∑

i∈A(a) xia ≤ Ca

I When page arrives, assign an eligible ad.I revenue from assigning page i to ad a: bia

I “AdWords” (AW) problem:I Maximize revenue of ads served: max

∑i,a biaxia

I Budget of ad a:∑

i∈A(a) biaxia ≤ Ba

General Form of LP

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

siaxia ≤ Ca (∀ a)

xia ≥ 0 (∀ i , a)

Online Matching:via = sia = 1

Disp. Ads (DA):sia = 1

AdWords (AW):sia = via

Worst-Case Greedy: 12 ,

[KVV]: 1− 1e -aprx

[MSVV,BJN]:1− 1

e -aprx

General Form of LP

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≥ 0 (∀ i , a)

Worst-Case Greedy: 12 ,

[MSVV,BJN]:1− 1

e -aprx

Ad Allocation: Problems and Models

Worst Case Greedy: 12 ,

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

[FMMM09,MOS11]:0.702-aprxi.i.d with knowndistribution

[DH09]:1−ε-aprx,ifopt max via

Stochastic i.i.d model:

I i.i.d model with known distribution

I random order model (i.i.d model with unknown distribution)

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

[FMMM09]:0.67-aprxi.i.d with knowndistribution

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

[FHKMS10,AWY]:1−ε-aprx,if opt max viaand Ca max sia

random order = i.i.d. model with unknown distribution

Stochastic DA: Dual Algorithm

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≤ Ca (∀ a)

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

zi ≥ via − βa (∀i , a)

βa, zi ≥ 0 (∀i , a)

Feldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt

m log n ), and large

capacity (Ca ≥ m log nε3

Fact: If optimum β∗a are known, this alg. finds optI Proof: Comp. slackness. Given β∗a , compute x∗ as follows:

x∗ia = 1 if a = argmax(via − β∗a).

Stochastic DA: Dual Algorithm

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≤ Ca (∀ a)

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

zi ≥ via − βa (∀i , a)

βa, zi ≥ 0 (∀i , a)

Algorithm:I Observe the first ε fraction sample of impressions.I Learn a dual variable for each ad βa, by solving the dual

program on the sample.I Assign each impression i to ad a that maximizes via − βa.

Feldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt

Stochastic DA: Dual AlgorithmFeldman, Henzinger, Korula, M., Stein 2010Thm[FHKMS10,AWY]: W.h.p, this algorithm is a (1−O(ε))-aprx,as long as each item has low value (via ≤ εopt

Lemma: In the random order model, W.h.p., the sample β′a areclose to β∗a .

I Extending DH09.

General Stochastic Packing LPs

I m fixed resources with capacity Ca

I Items i arrive online with options Oi , values vio , rsrc. use sioa.I Choose o ∈ Oi , using up capacity sioa in all a.

Thm[FHKMS10,AWY]: W.h.p, the PD algorithm is a(1−O(ε))-aprx, as long as items have low value (vio ≤ εopt

log n ) and

small size (sioa ≤ ε3Calog n ).

Other Results and Extensions (random order model):

I Agrawal, Wang, Ye: Updating dual variables by periodicsolution of the dual program: Ca ≥ m log n

ε2or sioa ≤ ε2Ca

I Vee, Vassilvitskii , Shanmugasundaram 2010: extension toconvex objective functions: Using KKT conditions.

log n ) and

?[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

Free Disposal[FKMMP09]:1− 1

e -aprx:if Ca max sia

[MSVV,BJN]:1− 1

e -aprx

Stochastic(i.i.d.)

DA: Free Disposal Model

0.07Ad 1: C1 = 1

I Advertisers may not complain about extra impressions, but nobonus points for extra impressions, either.

0.07Ad 1: C1 = 1

I Value of advertiser = sum of values of top Ca items she gets.

Greedy Algorithm

Assign impression to an advertisermaximizing Marginal Gain = (imp. value - min. impression value).

I Competitive Ratio: 1/2. [NWF78]I Follows from submodularity of the value function.

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

Evenly Split?

Greedy Algorithm

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

Evenly Split?

Greedy Algorithm

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n

n copiesn copies

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

Evenly Split?

Greedy Algorithm

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

Evenly Split?

Greedy Algorithm

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

Evenly Split?

A better algorithm?

Assign impression to an advertiser amaximizing (imp. value - βa),

where βa = average value of top Ca impressions assigned to a.

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

I Competitive Ratio: 12 if Ca >> 1. [FKMMP09]

I Primal-Dual Approach.

A better algorithm?

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

A better algorithm?

1 + ε

Ad 1: C1 = n

Ad 2: C2 = n1

n copiesn copies

n copies

An Optimal Algorithm

Assign impression to an advertiser a:maximizing (imp. value - βa),

I Greedy: βa = min. impression assigned to a.

I Better (pd-avg): βa = average value of top Ca impressionsassigned to a.

I Optimal (pd-exp): order value of edges assigned to a:v(1) ≥ v(2) . . . ≥ v(Ca):

βa =1

Ca(e − 1)

Ca∑j=1

v(j)(1 +1

Ca)j−1.

I Thm: pd-exp achieves optimal competitive Ratio: 1− 1e − ε if

Ca > O(1ε ). [Feldman, Korula, M., Muthukrishnan, Pal 2009]

βa =1

Ca(e − 1)

Ca∑j=1

v(j)(1 +1

Ca)j−1.

βa =1

Ca(e − 1)

Ca∑j=1

v(j)(1 +1

Ca)j−1.

Online Generalized Assignment (with free disposal)

I Multiple Knapsack: Item i may have different value (via) anddifferent size sia for different ads a.

I DA: sia = 1, AW: via = sia.

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

siaβa + zi ≥ via (∀i , a)

βa, zi ≥ 0 (∀i , a)

I Offline Optimization: 1− 1e − δ-aprx[FGMS07,FV08].

I Thm[FKMMP09]: There exists a 1− 1e − ε-approximation

algorithm if Camax sia

≥ 1ε .

Online Generalized Assignment (with free disposal)

I Multiple Knapsack: Item i may have different value (via) anddifferent size sia for different ads a.

I DA: sia = 1, AW: via = sia.

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

βa, zi ≥ 0 (∀i , a)

I Offline Optimization: 1− 1e − δ-aprx[FGMS07,FV08].

I Thm[FKMMP09]: There exists a 1− 1e − ε-approximation

algorithm if Camax sia

≥ 1ε .

Proof Idea: Primal-Dual Analysis [BJN]

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

βa, zi ≥ 0 (∀i , a)

I Proof:

1. Start from feasible primal and dual (xia = 0, βa = 0, andzi = 0, i.e., Primal=Dual=0).

2. After each assignment, update x , β, z variables and keepprimal and dual solutions.

3. Show ∆(Dual) ≤ (1− 1e )∆(Primal).

Proof Idea: Primal-Dual Analysis [BJN]

max∑i ,a

viaxia∑a

xia ≤ 1 (∀ i)∑i

xia ≥ 0 (∀ i , a)

min∑a

Caβa +∑i

βa, zi ≥ 0 (∀i , a)

I Proof:

1. Start from feasible primal and dual (xia = 0, βa = 0, andzi = 0, i.e., Primal=Dual=0).

2. After each assignment, update x , β, z variables and keepprimal and dual solutions.

3. Show ∆(Dual) ≤ (1− 1e )∆(Primal).

Free Disposal[FKMMP09]:1− 1

e -aprx: ifCa max sia

[MSVV,BJN]:1− 1

e -aprx

Stochastic(randomarrivalorder)

[FMMM09,MOS11]:0.702-aprx

I Online Stochastic Assignment ProblemsI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental EvaluationI Online Stochastic Weighted Matching

Dual-based Algorithms in Practice

I Algorithm:I Assign each item i to ad a that maximizes via − βa.

I More practical compared to Primal Algorithms:I Just keep one number βa per advertiser.I Suitable for Distributed Ad Serving Schemes.

I Training-based AlgorithmsI Compute βa based on historical/sample data.

I Hybrid approach (see also [MNS07]):I Start with trained βa (past history), blend in online algorithm.

Experiments: setup

I Real ad impression data from several large publishers

I 200k - 1.5M impressions in simulation period

I 100 - 2600 advertisers

I Edge weights = predicted click probability

I Efficiency: free disposal modelI Algorithms:

I greedy: maximum marginal valueI pd-avg, pd-exp: pure online primal-dual from [FKMMP09].I dualbase: training-based primal-dual [FHKMS10]I hybrid: convex combo of training based, pure online.I lp-weight: optimum efficiency

Experimental Evaluation: Summary

Algorithm Avg Efficiency%opt 100

greedy 69pd-avg 77pd-exp 82

dualbase 87hybrid 89

I pd-exp & pd-avg outperform greedy by 9% and 14% (withmore improvements in tight competition.)

I dualbase outperforms pure online algorithms by 6% to 12%.

I Hybrid has a mild improvement of 2% (up to 10%).

I pd-avg performs much better than the theoretical analysis.

Other Metrics: Fairness

I Qualititative definition: advertisers are “treated equally.”

I One suggestion[FHKMS10]: Compute ”fair” solution x∗,measure `1 distance to x∗.

I Fair solution:I Each a chooses best Ca impressions (highest via)I Repeat:

I Impressions shared among those who chose them.I If some a not receiving Ca imps, a chooses an additional imp.

Experiments: highlights

40 50 60 70 80 90 100

Efficiency

dualbasegreedy

hybrid

lp_weight

pd−avg

pd−exp

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Advertiser

lp−weightfairdualbasepd−avg

Experiments: highlights

70 75 80 85 90 95 100

Efficiency

dualbasegreedy hybrid

lp_weight

pd−avg

pd−exp

fair1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Advertiser

lp−weightfairdualbasepd−avg

In Production

I Smooth Delivery of Display AdsI Delivery of impressions throughout time should follow the

traffic smoothly.I Model this with multiple nested capacity constraints:

1− 1/e-competitive algorithm for this extension.I Bhalgat, Feldman, M., 2011

I Combined Allocation with Ad ExchangeI Yield Optimization of Display Advertising with Ad ExchangeI Belsairo, Feldman, M., Muthukrishnan, 2011

I Re-act adaptively and quickly to changes in traffic:I Use a control loop on the dual variable.I Assymptotically optimal policy: B. Tan and R. Srikant, 2011

In Production

Online Ad Allocation: Interesting Problems

I Online Stochastic DAI Simultaneous online worst-case & stochastic optimization.I Tradeoff between delivery penalty and efficiency: Covering

Constraints?I More complex stochastic modeling (drift, seasonality, etc.)

I Online Stochastic Ad AllocationI Online Stochastic PackingI Online Generalized Assignment (with free disposal)I Experimental ResultsI Online Stochastic Weighted Matching

Online Stochastic Weighted Matching

“ALG is α-approximation?” if E [ALG(H)]E [OPT(H)] ≥ α

Power of Two ChoicesI Offline:

1. Find an optimal fractional solution x∗e to a discountedmatching LP, where xe ≤ 1− 1

e .2. Sample a matching Ms from x∗.3. Let M ′ = M1\Ms where M1 is the maximum weighted

matching.

I Online: try the edge in Ms first, and if it doesn’t work, try M ′.

I Thm: Approximation factor is better than 0.66.

(Haeupler, M., ZadiMoghaddam, 2011).

Online Stochastic Weighted Matching

“ALG is α-approximation?” if E [ALG(H)]E [OPT(H)] ≥ α

Power of Two ChoicesI Offline:

1. Find an optimal fractional solution x∗e to a discountedmatching LP, where xe ≤ 1− 1

e .2. Sample a matching Ms from x∗.3. Let M ′ = M1\Ms where M1 is the maximum weighted

matching.

I Online: try the edge in Ms first, and if it doesn’t work, try M ′.

I Thm: Approximation factor is better than 0.66.

(Haeupler, M., ZadiMoghaddam, 2011).

Open Problems

I Online Stochastic Display Ad AllocationI Simultaneous online worst-case & stochastic optimization.I Tradeoff between delivery penalty and efficiency: Covering

Constraints?I More complex stochastic modeling (drift, seasonality, etc.)

I Online Stochastic Weighted MatchingI Online Stochastic Matching: Close gap between 0.703 & 0.81.I Online Stochastic Weighted Matching: Power of many

choices? Better lower bound?I Online Weighted Matching (with Free Disposal): Is

1− 1/e-approximation possible?

I Targeting.I Online Allocation

Planning:

Display Ad Delivery

Online, Stochastic

Demand for ads

Ad Planning: Research Issues

Which set of contracts should we accept?

Related Research Issues.I Pricing Uncertain Inventory.

I Stochastic Supply and DemandI Bundling Opportunities

I Online Mechanisms for Signing Contracts.

I Contracts with Delivery Penalty.

I Offline Optimization of Contracts.

Ad Planning: Research Issues

Which set of contracts should we accept?Related Research Issues.

I Pricing Uncertain Inventory.I Stochastic Supply and DemandI Bundling Opportunities

I Online Mechanisms for Signing Contracts.

I Contracts with Delivery Penalty.

I Offline Optimization of Contracts.

General Ad Planning: Weighted Matching

I n advertisers, and set Y of impressions (items).I Each advertiser i

I Interested in a set Ji of impressions, (e.g, young women inSeattle),

I Needs di impressions (Demand),I Value vit (or Bid bi ) for each impression t,

Jjdi = 4

biAdvertisers

Impressions

(Ji, bi, di)

Efficiency (or Revenue) Maximization: Find an assignment withthe maximum value.

Contracts with Delivery Penalty

If we don’t meet the demand of an advertiser this month, weshould give him/her free impressions in the next month.

I Each advertiser iI Needs di impressions,I Bids bi for each impression,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).

Contracts with Delivery Penalty

If we don’t meet the demand of an advertiser this month, weshould give him/her free impressions in the next month.

I Each advertiser iI Needs di impressions,I Bids bi for each impression,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).

Ad Planning With Penalties

I Interested in set Ji of impressions, (e.g, young women inSeattle),

I Bids bi for each impression,I Needs di impressions,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).

Jjdi = 4

biAdvertisers

Impressions

(Ji, bi, di)

Goal: Choose a set T of advertisers to maximize revenue, f (T ).

Ad Planning With Penalties

I Interested in set Ji of impressions, (e.g, young women inSeattle),

I Bids bi for each impression,I Needs di impressions,I Penalty λbi for not satisfying each unit (Guaranteed Delivery).

Jjdi = 4

biAdvertisers

Impressions

(Ji, bi, di)

Goal: Choose a set T of advertisers to maximize revenue, f (T ).

Relation to Weighted MatchingIf we give q items to advertiser i , we get

qbi − λbi (di − q) = q(1 + λ)bi − diλbi = q(1 + λ)bi − ci

If we commit to a set T of advertisers:

f (T ) = P(T )−∑

i∈T ci = P(T )− C (T ).

I C (T ) =∑

i∈T ci where ci = diλbi .

I P(T ) be the maximum weighted matching in the followingbipartite graph with (1 + λ)bi as weights of edges.

I Advertiser i ∈ T needs at most di ads.I Each ad can go to at most one advertiser.

Advertisers

Impressions

Maximum weighted matching for this graph.

(1 + λ)bj(1 + λ)bi

P (T ) =

Relation to Weighted MatchingIf we give q items to advertiser i , we get

qbi − λbi (di − q) = q(1 + λ)bi − diλbi = q(1 + λ)bi − ci

If we commit to a set T of advertisers:

f (T ) = P(T )−∑

i∈T ci = P(T )− C (T ).

I C (T ) =∑

i∈T ci where ci = diλbi .

I P(T ) be the maximum weighted matching in the followingbipartite graph with (1 + λ)bi as weights of edges.

I Advertiser i ∈ T needs at most di ads.I Each ad can go to at most one advertiser.

Advertisers

Impressions

Maximum weighted matching for this graph.

(1 + λ)bj(1 + λ)bi

P (T ) =

Discussion Summary

Given a set T of advertisers, maximizing f (T ) is easy as it is amaximum weighted matching.

Challenge: Which set of advertisers T should we accept tomaximize f (T )?

I Offline Optimization.

I Can be used in a negotiation process.

I Can have different penalty factors λi for each advertiser i .

Discussion Summary

Ad Planning with Penalties

Feige, Immorlica, M., Nazerzadeh, 2008.

I Hardness: No Constant-factor Approximation.I Heuristic Greedy Algorithms:

I Simple Greedy Algorithm: Bicriteria Approximation.I At each step, add the advertiser with the maximum

profit-per-impression fixing the existing assignment.

Theorem: This is a good approximation compared to theoptimum with larger penalty factor.

I Greedy-Rate Algorithm: Structural Approximation.

Greedy Algorithms

Greedy-Rate Algorithm:

I At each step, add the advertiser with the maximummarginal-profit per marginal-cost ratio.

T : Set of advertisers we committed to (initialized to ∅)I At each step, add an advertiser i ∈ X\S to T that maximizes

P(S∪i)−P(S)ci

, if P(S ∪ i)− P(S)− ci > 0.

Theorem: The greedy-rate algorithm achieves the best structuralapproximation.Proof: Uses submodularity of P(T ), and f (T ).

I The approximation factor of the algorithm is a function of the

structure of the solution, i.e., a Signature: α = C(OPT)

P(OPT).

I Greedy-rate algorithm achieves at least factor1−α−α ln 1

α1−α

(improving factor 1 + α− 2√α).

Greedy Algorithms

P(S∪i)−P(S)ci

, if P(S ∪ i)− P(S)− ci > 0.

P(OPT).

α1−α

Greedy Algorithms

P(S∪i)−P(S)ci

, if P(S ∪ i)− P(S)− ci > 0.

Theorem: The greedy-rate algorithm achieves the best structuralapproximation.

Proof: Uses submodularity of P(T ), and f (T ).

P(OPT).

α1−α

Greedy Algorithms

P(S∪i)−P(S)ci

, if P(S ∪ i)− P(S)− ci > 0.

P(OPT).

α1−α

Ad Planning with Delivery Penalty

Online

Banner Ad Delivery

Planning:Which

ads/advertisersshould wecommit to?

Strategic

Stochastic

FIMN’08

Constraints: Guaranteed Delivery, Fairness, ...

BHK 09

CFMP 09

Banner Ad Delivery

• Babaiof, Hartline, Kleinberg: Online Algorithms with Buyback

• Special cases: Single item, Matroid, Knapsack

• Constantin, Feldman, Muthkrishnan, Pal: Ad slotting with Cancellations.

• Special case: Demand=1, Truthful Mechanism: Constant-factor

Interesting Algorithmic Problem:I Online mechanism for general ad planning with delivery

penalty: bicriteria approximation?

Ad Planning with Delivery Penalty

Online

Banner Ad Delivery

Planning:Which

ads/advertisersshould wecommit to?

Strategic

Stochastic

FIMN’08

Constraints: Guaranteed Delivery, Fairness, ...

BHK 09

CFMP 09

Banner Ad Delivery

• Babaiof, Hartline, Kleinberg: Online Algorithms with Buyback

• Special cases: Single item, Matroid, Knapsack

• Constantin, Feldman, Muthkrishnan, Pal: Ad slotting with Cancellations.

• Special case: Demand=1, Truthful Mechanism: Constant-factor

Interesting Algorithmic Problem:I Online mechanism for general ad planning with delivery

penalty: bicriteria approximation?

Ad Planning: Offline Optimization of Contracts

I Fast Algorithms to Verify Feasibility of Contracts:I Lopsided Bipartite Graphs.I Improved Algorithms for Bipartite Network Flow: Ahuja, Orlin,

Stein, Tarjan 94I Faster Algorithm for max-flow: running time depends on the

size of smaller part.

I Sampling for Max-Cardinality Matching: Charles, Chickering,Devanur, Jain, Sanghi 2010,

I Sampling and Concise Allocation.I Algorithm: Iteratively assign nodes, and minimize the future

failure probability.I WHP verifies if there exists a feasible matching.

I Online algorithms for accepting contracts: Alaei, Arcuate,Khuller, Ma, Malekian, Tomlin 2009

I Utility model to combine contract-based advertisers &sales-based advertisers.

I Online algorithm for accepting contracts (under assumptions)

I Ad delivery for contract based settingsI PlanningI Ad Serving

Three main theory/practice problems

Combined Allocation with AdX: Objective

Short-term: boost revenue from AdXVS

Long-term: prioritize quality of guaranteed contracts.

Find allocation policy to maximize

yield = revenue(AdX) + γ · quality(advertisers),

where γ ≥ 0 is a tradeoff paramater (or Lagrange multiplier).

Publisher’s Decisions

Impression n-tharrives withquality Qn

Assign to an advertiser or discard

Submit to AdXwith price p

Obtain payment

Assign to anadvertiser ordiscard

accept

reject

Optimal to always test the exchange!

Publisher’s Decisions

Impression n-tharrives withquality Qn

Assign to an advertiser or discard

Submit to AdXwith price p

Obtain payment

Assign to anadvertiser ordiscard

accept

reject

Optimal to always test the exchange!

Impact of AdX

350 370 390 410 430 450

Quality

Advert

Revenue AdX

Pareto efficient frontier

I γ = 0: maximum revenue from AdX.

I γ =∞: maximum placement quality for contracts.

Display Ad Delivery

Planning:

Display Ad Delivery

Online, Stochastic

Demand for ads

Display Ad Delivery

Planning:

Display Ad Delivery

Online, Stochastic

Offline, Online

Feedback

Forecasting

Demand for ads

Online Learning & Allocation

I Value: Estimated Click-Through-Rate (CTR).

I Combined online capacity planning & learning?I Budgeted Active Learning

I Madani, Lizotte, Greiner 2004, Active Model Selection.

I Bayesian Budgeted Multi-armed Bandits:I Guha, Munagala, Multi-armed Bandits with Metric Switching

Costs.I Goel, Khanna, Null, The Ratio Index for Budgeted Learning,

with Applications.I Guha, Munagala, Pal, Multi-armed Bandit with Delayed

Feedback.

I Budgeted Unknown-CTR Multi-armed BanditI Pandey, Olston 2007, Handling Advertisement of Unknown

Quality.

I Value: Estimated Click-Through-Rate (CTR).I Combined online capacity planning & learning?

I Budgeted Active LearningI Madani, Lizotte, Greiner 2004, Active Model Selection.

Feedback.

Quality.

Feedback.

Quality.

Feedback.

Quality.

Online CTR Learning: Mixed Explore/Exploit

I Pandey, Olston 2007, Handling Advertisement of UnknownQuality.

I Algorithm: Revised GreedyI Upon arrival of query of type i , assign it to an ad a maximizing

Pia = (cia +√

2 ln ninia

where cia is the current estimate of CTR, nia is the number oftimes i has been assigned to a, ni is the number of queries oftype i so far.

I Thm[PO07]: ALG ≥ opt2 − O(ln n) where n is the number of

arrivals.

Pia = (cia +√

2 ln ninia

arrivals.

Pia = (cia +√

2 ln ninia

arrivals.

Hybrid ad serving: Contracts + Spot Auctions

Given a page view, and two types of advertisers:

I Contract-based.

I Auction-based.

I Decide who wins and how much do they pay.I Requirements:

I For each contract-advertiser, meet its demand.I Implement the scheme using proxy-bidding for

contract-advertisers in the spot auction.

Given a page view, and two types of advertisers:

I Contract-based.

I Auction-based.

I Decide who wins and how much do they pay.I Requirements:

I For each contract-advertiser, meet its demand.I Implement the scheme using proxy-bidding for

contract-advertisers in the spot auction.

I Naive solution: If a contract-adv is eligible and has notfinished demand, then let it win the spot. Bid infinity for allauctions.

I Optimize for revenue: If the auction pressure (price) is lowthen let the contract-adv win. Bid a low bid for all auctions.

I Unfair to contract-adv, since low auction-price ⇒ it is a lowervalue impression.

I Ideally:I Provide contract-adv with a representative allocation, an equal

slice of impressions from each price-point.I A price-oblivious scheme, i.e., bid without seeing the auction

bids.I Revenue per auction: average auction-price of impressions

given away to contract-advertisers is at most some target t.

Obtaining representative allocationsTwo main ideas:

1. Can implement any decreasing function a(p) for fraction ofimpressions of auction-price p.

2. Solve the system for well chosen distance functions:

Minimize dist(U, a)

∫pa(p)f (p)dp = d∫

ppa(p)f (p)dp ≤ td

Obtaining representative allocationsTwo main ideas:

1. Can implement any decreasing function a(p) for fraction ofimpressions of auction-price p.

2. Solve the system for well chosen distance functions:

Minimize dist(U, a)

∫pa(p)f (p)dp = d∫

ppa(p)f (p)dp ≤ td

Online Learning & Auction Incentives

[Devanur,Kakade’09, Babaioff,Sharma,Slivkins’09]

I Multi-Armed Bandit algorithms achieve an “implicit”exploration-exploitation tradeoff to get a regret of O(

√T )

(e.g., UCB).

I Can these be run in tandem with truthful auctions? (e.g., 2ndprice for a single slot).

I A naive explore-exploit method gets O(T 2/3) regret:I Explore ads for the first phase, giving them out for free.I Fix the CTRs thus learned in the first phase.I Run 2nd price auction for the 2nd phase.

I Can you do better that this simpe decoupling?

Theorem[DK09,BSS09] For every truthful auction (under certainassumptions), there exist bids, ctrs, s.t. regret = Ω(T 2/3).

√T )

(e.g., UCB).

√T )

(e.g., UCB).

Display Ad Delivery

Planning:

Display Ad Delivery

Online, Stochastic

Offline, Online

Feedback

Forecasting

Demand for ads

Open Problems:I Optimal combined online allocation & learning.I Feature selection and correlation in learning CTR.I Optimal combined stochastic planning and serving?

Thank You

online ad serving: theory and practice - sigmetrics

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