Bandits for Taxonomies: A Model-based

Approach

Sandeep PandeyDeepak Agarwal

Deepayan ChakrabartiVanja Josifovski

The Content Match Problem

Adv

ertis

ers

Ads DB

Ads

Ad impression: Showing an ad to a user

(click)

The Content Match Problem

Adv

ertis

ersAds

Ad click: user click leads to revenue for ad server and content provider

Ads DB

(click)

The Content Match Problem

Adv

ertis

ers

Ads DB

Ads

The Content Match Problem:

Match ads to pages to maximize clicks

The Content Match Problem

Adv

ertis

ers

Ads DB

Ads

Maximizing the number of clicks means: For each webpage, find the ad with the best Click-Through Rate (CTR), but without wasting too many impressions in learning this.

Online Learning

Maximizing clicks requires: Dimensionality reduction Exploration Exploitation

Both must occur together

Online learning is needed, since the system must continuously generate revenue

Taxonomies for dimensionality reduction

Root

Apparel Computers Travel

• Already exist

• Actively maintained

• Existing classifiers to map pages and ads to taxonomy nodes

Page/Ad

Learn the matching from page nodes to ad nodes dimensionality reduction

Online Learning

Maximizing clicks requires: Dimensionality reduction Exploration Exploitation

Can taxonomies help in explore/exploit as well?

Taxonomy

?

Outline

ProblemBackground: Multi-armed bandits

Proposed Multi-level Policy Experiments Related Work Conclusions

Background: Bandits

Bandit “arms”

p1 p2 p3(unknown payoff

probabilities)

Pull arms sequentially so as to maximize the total expected reward

• Estimate payoff probabilities pi

• Bias the estimation process towards better arms

Background: BanditsW

ebpa

ge 1

Bandit “arms”

Web

page

2W

ebpa

ge 3

= ads

~106 ads

~109 pages

Background: BanditsAds

Web

page

s

Content Match = A matrix

• Each row is a bandit

• Each cell has an unknown CTR

One bandit

Unknown CTR

Background: Bandits

Bandit Policy

1. Assign priority to each arm

2. “Pull” arm with max priority, and observe reward

3. Update priorities

Priority 1

Priority 2

Priority 3

Allocation

Estimation

Background: Bandits

Why not simply apply a bandit policy directly to our problem?

• Convergence is too slow ~109 bandits, with ~106 arms per bandit

• Additional structure is available, that can help Taxonomies

Outline

ProblemBackground: Multi-armed banditsProposed Multi-level Policy

Experiments Related Work Conclusions

Multi-level PolicyAds

Webpages

… …

……

……

classes

classes

Consider only two levels

Multi-level PolicyApparel

Compu-ters Travel

… …

……

……

Consider only two levels

Trav

elC

ompu

-te

rsA

ppar

elAd parent classes

Ad child classes

Block

One bandit

Multi-level PolicyApparel

Compu-ters Travel

… …

……

……

Key idea: CTRs in a block are homogeneous

Ad parent classes

Block

One bandit

Trav

elC

ompu

-te

rsA

ppar

el

Ad child classes

Multi-level Policy CTRs in a block are

homogeneous Used in allocation (picking ad for

each new page) Used in estimation (updating

priorities after each observation)

Multi-level Policy CTRs in a block are

homogeneousUsed in allocation (picking ad for each new page)

Used in estimation (updating priorities after each observation)

C

A C T

AT

Multi-level Policy (Allocation)

?

Page classifier

Classify webpage page class, parent page class Run bandit on ad parent classes pick one ad parent

class

C

A C T

AT

Multi-level Policy (Allocation)

Classify webpage page class, parent page class Run bandit on ad parent classes pick one ad parent

class Run bandit among cells pick one ad class In general, continue from root to leaf final ad

?

Page classifier

ad

C

A C T

AT

ad

Multi-level Policy (Allocation)

Bandits at higher levels use aggregated information have fewer bandit arms Quickly figure out the best ad parent

class

Page classifier

Multi-level Policy CTRs in a block are

homogeneousUsed in allocation (picking ad for each new page)Used in estimation (updating priorities after each observation)

Multi-level Policy (Estimation) CTRs in a block are

homogeneous Observations from one cell also

give information about others in the block

How can we model this dependence?

Multi-level Policy (Estimation) Shrinkage Model

Scell | CTRcell ~ Bin (Ncell, CTRcell)

CTRcell ~ Beta (Paramsblock)

# clicks in cell# impressions

in cell

All cells in a block come from the same distribution

Multi-level Policy (Estimation) Intuitively, this leads to

shrinkage of cell CTRs towards block CTRs

E[CTR] = α.Priorblock + (1-α).Scell/Ncell

Estimated CTR

Beta prior (“block CTR”)

Observed CTR

Outline

ProblemBackground: Multi-armed banditsProposed Multi-level PolicyExperiments

Related Work Conclusions

Experiments

Root

20 nodes

221 nodes…

~7000 leaves

Taxonomy structure

We use these 2 levels

Depth 0

Depth 7

Depth 1

Depth 2

Experiments Data collected over a 1 day period Collected from only one server, under some

other ad-matching rules (not our bandit) ~229M impressions CTR values have been linearly transformed

for purposes of confidentiality

Experiments (Multi-level Policy)

Multi-level gives much higher #clicks

Number of pulls

Clic

ks

Experiments (Multi-level Policy)

Multi-level gives much better Mean-Squared Error it has learnt more from its explorations

Mea

n-S

quar

ed E

rror

Number of pulls

Experiments (Shrinkage)

Number of pulls Number of pullsMea

n-S

quar

ed E

rror

Clic

ks without shrinkage

with shrinkage

Shrinkage improved Mean-Squared Error, but no gain in #clicks

Outline

ProblemBackground: Multi-armed banditsProposed Multi-level PolicyExperimentsRelated Work

Conclusions

Related Work Typical multi-armed bandit problems

Do not consider dependencies Very few arms

Bandits with side information Cannot handle dependencies among ads

General MDP solvers Do not use the structure of the bandit problem Emphasis on learning the transition matrix, which

is random in our problem.

Conclusions Taxonomies exist for many datasets They can be used for

Dimensionality Reduction Multi-level bandit policy higher #clicks Better estimation via shrinkage models better

MSE