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## PowerPoint Slideshow about 'Hybrid Keyword Auctions' - johana

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### Hybrid Keyword Auctions

Ashish Goel

Stanford University

Joint work with Kamesh Munagala, Duke University

Online Advertising

Pricing Models

- CPM (Cost per thousand impressions)
- CPC (Cost per click)
- CPA (Cost per acquisition)
- Conversion rates:
- Click-through-rate (CTR), conversion from clicks to acquisitions, …

Differences between these pricing models:

- Uncertainty in conversion rates:
- Sparse data, changing rates, …
- Stochastic fluctuations:
- Even if the conversion rates were known exactly, the number of clicks/conversions would still vary, especially for small samples

Cost-Per-Click Auction

CTR estimate

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

Q

C

- Value/impression ordering: C1Q1 > C2Q2 > …
- Give impression to bidder 1 at CPC = C2Q2/Q1

Cost-Per-Click Auction

CTR estimate

Auctioneer

(Search Engine)

Bid = Cost per Click

Advertiser

Q

C

- Value/impression ordering: C1Q1 > C2Q2 > …
- Give impression to bidder 1 at CPC = C2Q2/Q1

- VCG Mechanism: Truthful for a single slot, assuming static CTR estimates
- Can be made truthful for multiple slots [Vickrey-Clark-Groves, Myerson81, AGM06]
- This talk will focus on single slot for proofs/examples

When Does this Work Well?

- High volume targets (keywords)
- Good estimates of CTR
- What fraction of searches are to high volume targets?
- Folklore: a small fraction
- Motivating problem:
- How to better monetize the low volume keywords?

Possible Solutions

- Coarse ad groups to predict CTR:
- Use performance of advertiser on possibly unrelated keywords
- Predictive models
- Regression analysis/feature extraction
- Taxonomies/clustering
- Collaborative filtering
- Learn the human brain!
- Our approach: Richer pricing models + Learning

Hybrid Scheme: 2-Dim Bid

M = Cost per Impression

C= Cost per Click

Auctioneer

(Search Engine)

Advertiser

<M,C >

Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

- Advertiser’s score Ri = max { Mi , Ci Qi }

Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

- Advertiser’s score Ri = max { Mi , Ci Qi }
- Order by score: R1 > R2 > …

Hybrid Scheme

M = Cost per Impression

C= Cost per Click

CTR estimate

Auctioneer

(Search Engine)

Advertiser

Q

<M,C >

- Advertiser’s score Ri = max { Mi , Ci Qi }
- Order by score: R1 > R2 > …
- Give impression to bidder 1:
- If M1 > C1Q1then chargeR2per impression
- If M1 < C1Q1then chargeR2 / Q1per click

Example: CPC Auction

Bidder 1

Bidder 2

Per click cost C

5

10

Conversion rate

estimate Q

0.1

0.08

0.5

0.8

C * Q

CPC auction allocates to bidder 2 at CPC = 0.5/0.08 = 6.25

Example: Hybrid Auction

Bidder 1

Bidder 2

Per click cost C

5

10

Conversion rate

estimate Q

0.1

0.08

0.5

0.8

C * Q

Per impression

cost M

0

1.0

Max {M, C * Q}

1.0

0.8

Hybrid auction allocates to bidder 1 at CPI = 0.8

Why Such a Model?

- Per-impression bid:
- Advertiser’s estimate or “belief” of CTR
- May or may not be an accurate reflection of the truth
- Backward compatible with cost-per-click (CPC) bidding

Why Such a Model?

- Per-impression bid:
- Advertiser’s estimate or “belief” of CTR
- May or may not be an accurate reflection of the truth
- Backward compatible with cost-per-click (CPC) bidding
- Why would the advertiser know any better?
- Advertiser aggregates data from various publishers
- Has domain specific models not available to auctioneer
- Is willing to pay a premium for internal experiments

Provable Benefits

- Search engine:Better monetization of low volume keywords
- Typical case: Unbounded gain over CPC auction
- Pathological worst case: Bounded loss over CPC auction
- Advertiser: Opportunity to make the search engine converge to the correct CTR estimate without paying a premium
- Technical:
- Truthful
- Accounts for risk characteristics of the advertiser
- Allows users to implement complex strategies

Multiple Slots

- Show the top K scoring advertisers
- Assume R1 > R2 > … > RK > RK+1…
- Generalized Second Price (GSP) mechanism:
- For the ith advertiser, if:
- IfMi > QiCithen charge Ri+1per impression
- IfMi < QiCithen charge Ri+1 / Qi per click

Multiple Slots

- Show the top K scoring advertisers
- Assume R1 > R2 > … > RK > RK+1…
- Generalized Second Price (GSP) mechanism:
- For the ith advertiser, if:
- IfMi > QiCithen charge Ri+1per impression
- IfMi < QiCithen charge Ri+1 / Qi per click
- Can also implement VCG [Vickrey-Clark-Groves, Myerson81, AGM06]
- Need separable CTR assumption
- Details in the paper

Uncertainty Model for CTR

- For analyzing advantages of Hybrid, we need to model:
- Available information about CTR
- Asymmetry in information between advertiser and auctioneer
- Evolution of this information over time
- We will use Bayesian model of information
- Prior distributions
- Specifically, Beta priors (more later)

Bayesian Model for CTR

True underlying CTR = p

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

Bayesian Model for CTR

True underlying CTR = p

Per-impression bid

M

CTR estimate

Q

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

Bayesian Model for CTR

True underlying CTR = p

Per-impression bid

M

CTR estimate

Q

Prior distribution Pauc

Prior distribution Padv

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

Each agent optimizes based on its current “belief” or prior:

Beliefs updated with every impression

Over time, become sharply concentrated around true CTR

What is a Prior?

- Simply models asymmetric information
- Sharper prior More certain about true CTR p
- E[ Prior ] need not be equal to p
- Main advantage of per-impression bids is when:
- Advertiser’s prior is “more resolved” than auctioneer’s
- Limiting case: Advertiser certain about CTRp
- Priors are only for purpose of analysis
- Mechanism is well-defined regardless of modeling assumptions

Truthfulness

- Advertiser assumes CTR follows distribution Padv
- Wishes to maximize expected profit at current step
- E[Padv]=x = Expected belief about CTR
- Click utility = C
- Expected profit = C x - Expected price

Truthfulness

- Advertiser assumes CTR follows distribution Padv
- Wishes to maximize expected profit at current step
- E[Padv]=x = Expected belief about CTR
- Click utility = C
- Expected profit = C x - Expected price

Bidding (Cx, C) is the dominant strategy

Regardless of Q used by auctioneer andtrue CTR p

Elicits advertiser’s “expected belief” about the CTR!

Holds in many other settings (more later)

Conjugate Beta Priors

- Auctioneer’s Paucfor advertiseri =Beta(,)
- ,are positive integers
- Conjugate of Bernoulli distribution (CTR)
- Expected value =/ ( + )

Conjugate Beta Priors

- Auctioneer’s Paucfor advertiseri =Beta(,)
- ,are positive integers
- Conjugate of Bernoulli distribution (CTR)
- Expected value =/ ( + )
- Bayesian update with each impression:
- Probability of click = / ( + )
- If click, new Pauc(posterior) =Beta(,)
- If no click, new Pauc(posterior) =Beta(,)

Evolution of Beta Priors

Denotes Beta(1,1)

Uniform prior

Uninformative

Click

1,1

No Click

1/2

1/2

2,1

1,2

2/3

1/3

1/3

2/3

E[Pauc]= 1/4

3,1

2,2

1,3

1/4

1/2

3/4

1/2

3/4

1/4

4,1

3,2

2,3

1,4

E[Pauc]= 2/5

Properties of Beta Priors

- Larger , Sharper concentration around p
- Uninformative prior: Beta(,)= Uniform[0,1]
- Q =E[Pauc] = / ( + )
- Auctioneer’s expected “belief” about CTR
- Could be different from true CTR p

Advertiser Certain of CTR

True underlying CTR = p

Per-impression bid

M = Cp

CTR estimate

Q = / ( + )

Pauc = Beta(,)

Knows p

(Public)

(Private)

Auctioneer

(Search Engine)

Advertiser

Properties of Auction

- Revenue properties for auctioneer:
- Typical case benefit:log n times better than CPC scheme
- Bounded pathological case loss: 36% of CPC scheme
- Unbounded gain versus bounded loss!
- Flexibility for advertiser:
- Can make Paucconverge to p without paying premium
- But pays huge premium for achieving this in CPC auction

Better Monetization

p1

Adv. 1

Q ≈ 1 / log n

Pauc = Beta (, log n)

p2

Adv. 2

Auctioneer

p3

Adv. 3

Pauc = Beta (, log n)

…

- Low volume keyword:
- Auctioneer’s prior has high variance
- Some pi close to 1 with high probability

pn

Adv. n

Better Monetization

- Hybrid auction: Per-impression bid elicits high pi
- CPC auction allocates slot to a random advertiser
- Theorem: Hybrid auction generates log n times more revenue for auctioneer than CPC auction

Flexibility for Advertisers

AssumeC = 1

Per-impression bid

M = p

Advertiser

Knows p

Q = / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Flexibility for Advertisers

Per-impression bid

M = p

Advertiser

Knows p

Q = / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Wins on per impression bid

Pays at most p per impression

Flexibility for Advertisers

T impressions

N clicks

Per-impression bid

M = p

Advertiser

Knows p

Makes Q converge to p

Q = / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Wins on per impression bid

Pays at most p per impression

Flexibility for Advertisers

T impressions

N clicks

Per-impression bid

M = p

Advertiser

Knows p

Makes Q converge to p

Q = / ( + )

Auctioneer

(Search Engine)

Pauc = Beta(,)

Now switch to CPC bidding

Flexibility for Advertisers

- If Q converges in T impressions resulting in N clicks:
- ( N T) ≥ p
- Since Q = /( + )< p, this implies N ≥ T p
- Value gain = N; Payment for T impressions at most T * p
- No loss in utility to advertiser!
- In the existing CPC auction:
- The advertiser would have to pay a huge premium for getting impressions and making the CTR converge

Uncertain Advertisers

- Advertiser “wishes” CTR p toresolve to a high value
- In that case, she can gain utility in the long run
- … but CTR resolves only on obtaining impressions!
- Should pay premium now for possible future benefit
- What should her dynamic bidding strategy be?

Uncertain Advertisers

- Advertiser “wishes” CTR p toresolve to a high value
- In that case, she can gain utility in the long run
- … but CTR resolves only on obtaining impressions!
- Should pay premium now for possible future benefit
- What should her dynamic bidding strategy be?
- Key contribution:
- Defining a new Bayesian model for repeated auctions
- Dominant strategy exists!

The Issue with Dynamics

Padv1

Adv. 1

Pauc1

Auctioneer

Pauc2

Padv2

Adv. 2

[Bapna & Weber ‘05, Athey & Segal ‘06]

- Advertiser 1 underbids so that:
- Advertiser 2 can obtain impressions
- Advertiser 2 may resolve its CTR to a low value
- Advertiser 1 can then obtain impressions cheaply

Semi-Myopic Advertiser

- Maximizes utility in contiguous time when she wins the auction
- Priors of other advertisers stay the same during this time
- Once she stops getting impressions, cannot predict future

… since future will depend on private information of other bidders!

Semi-Myopic Advertiser

- Maximizes utility in contiguous time when she wins the auction
- Priors of other advertisers stay the same during this time
- Once she stops getting impressions, cannot predict future

… since future will depend on private information of other bidders!

- Advertiser always has a dominant hybrid strategy
- Bidding Index: Computation similar to the Gittins index
- Advertiser can optimize her utility by dynamic programming
- Socially optimal in many reasonable scenarios
- Implementation needs both per-impression and per-click bids

Summary

- Allow both per-impression and per-click bids
- Same ideas work for CPM/CPC + CPA
- Significantly higher revenue for auctioneer
- Easy to implement
- Hybrid advertisers can co-exist with pure per-click advertisers
- Easy path to deployment/testing
- Many variants possible with common structure:
- Optional hybrid bids
- Impression + Click [S. Goel, Lahaie, Vassilvitskii, 2010]

Conclulsion and Open Questions

- Learning is important in Online advertising
- Remember that there are multiple strategic participants
- Design richer pricing and communication signals
- Some issues that need to be addressed:
- Whitewashing: Re-entering when CTR is lower than the default
- Fake Clicks: Bid per impression initially and generate false clicks to drive up CTR estimate Q
- Switch to per click bidding when slot is “locked in” by the high Q

Open Questions

- Some issues that need to be addressed:
- Whitewashing: Re-entering when CTR is lower than the default
- Fake Clicks: Bid per impression initially and generate false clicks to drive up CTR estimate Q
- Switch to per click bidding when slot is “locked in” by the high Q
- Analysis of semi-myopic model
- Other applications of separate beliefs?

Open Questions

- Some issues that need to be addressed:
- Whitewashing: Re-entering when CTR is lower than the default
- Fake Clicks: Bid per impression initially and generate false clicks to drive up CTR estimate Q
- Switch to per click bidding when slot is “locked in” by the high Q
- Analysis of semi-myopic model
- Other applications of separate beliefs?
- Connections of Bayesian mechanisms to:
- Regret bounds and learning [Nazerzadeh, Saberi, Vohra ‘08]
- Best-response dynamics [Edelman, Ostrovsky, Schwarz ‘05]

Truthfulness

- Advertiser assumes CTR follows distribution Padv
- Wishes to maximize expected profit at current step
- E[Padv]=x = Expected belief about CTR
- Utility from click = C
- Expected profit = C x - Expected price

Let Cy = Per impression bid

R2 = Highest other score

If max(Cy, C Q) <R2then Price = 0

Else:

If y < Q then: Price = x R2 / Q

If y > Q then: Price = R2

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