Working with Preferences

1
Working with Preferences

• Ronen Brafman
• Computer Science Department
• Stanford University

On leave from Ben-Gurion University
2
Goal Provide tools and build systems that are
able to make, or able to help users make, good
choices
3
Applications of Interest

• optimal product/item selection
• optimal product configuration
• guiding program choices
• personalization
• We target lay users with no background in
  decision theory

4
Goal of this Talk Provide an overview of an
approach to this problem based on the xCP-net
models and algorithms, and discuss some
applications
5
Constrained Optimization Process
Manufacturer Constraints
Feedback ? Spec Revision
Updated Choice
6
The Key Ideas

• Preference elicitation
• Use natural language like statements make it
  simple
• Support heterogeneous types of statements
• Make scaling up to quantitative assessment
  possible
• Calculating optimal choices
• Efficient methods for ordering sets
• Algorithms for constrained optimization
• Efficient data-driven incremental elicitation

7
Elicitation and Modeling
8
Natural Preferences Statements

• Value preferences
• Strict I prefer isle to window seats
• Conditional I prefer isle to window in economy
  class
• Attribute importance
• Strict Seat assignment is more important than
  airline
• Conditional Seat assignment is less important
  than airline in domestic flights

9
Ceteris Paribus Semantics

• Ceteris Paribus all else being equal
• I prefer isle to window seats ?
• Given two flights that differ only in seat
  assignment, I prefer the one with an isle seat.
• Otherwise, cant infer a preference
• Seat assignment is less important than airline
  in domestic flights ?
• Given two domestic flights that differ in seat
  assignment and airline only, I prefer the one
  with a better seat assignment
• Says nothing about two international flights

10
CP-nets (Boutilier, Brafman, Hoos, Poole, UAI 99)

• A qualitative, graphical model of preferences,
  that captures and organizes statements of
  conditional preferential independence.
• Each node represents a domain variable.
• Parents(v) are those variables that affect users
  preference over the values of v
• Parents(class) airline
• Conditional preference table (CPT) associated
  with every node in the CP-net
• Provides an ordering over the values of the node
  for every possible parent context

11
Example of a CP-net
12
Semantics and Consistency
Any acyclic CP-net defines a (consistent)
partial order over the outcome space.
13
Importance Relations
14
More Complex Example
Day of the flight
Airline
Departure Time
Stop-overs
Class
15
Day of the flight
Departure Time
Airline
Stop-over
Class
16
Day of the flight
Departure Time
Airline
Stop-overs
Class
17
nodes ? variables
cp-arcs (directed)
A
i-arcs (directed)
ci-arcs (undirected)
B
E
cp-tables
ci-tables
C
D
18
Role of Graphical Structure

• Users need not be aware of the underlying
  graphical structure
• User employs statement templates
• System constructs the network on the fly
• Graphical structure important for analysis and
  algorithms

19
UCP-Nets Boutilier, Bacchus, Brafman

• Quantified CPT
• Simplified semantics sum of utility factors
  U(abcd)
• fA(a)fB(b)fC(abc)fD(cd)
• 5 4 .2 .9 10.1
• Linear utility computation

a gt a 5 2
b gt b 4 3
c c
C
a b .6 .1 a b .2 .8 a b .3 .8 a b .9 .3
d d
c .9 .8 c .2 .3
D
20
UCP-nets Capture Heterogeneous Data

• Diverse statement compile into UCP-net
• Independence information maintained by graph
• Value preferences and variables preferences
• Two-way comparisons of complete outcomes
• Quantitative information
• Simple compilation based on linear constraints
• Good for incremental refinement
• Start with qualitative model no cold start!
• Refine with user feedback/additional observations

21
Using (T)CP-nets Algorithms

• Ordering sets/selecting top-element
• Preference-based constrained optimization

22
1. Ordering Elements

• Need Order (the many) results of a query
• Naïve solution pairwise comparison -- ogto ?
• Problem NP-hard in general
• Alternative solution linearize the partial order
• Insight some linearizations are easy to obtain
• Key
• One of oeo or oeo can be decided quickly
• Answers used to generate consistent ordering

23
2a. Preferential Optimization
Finding the preferentially optimal outcome for an
acyclic network is straightforward!
24
2b. Preference-Based Constrained Optimization
(PCO)

• Given
• user preferences
• an implicitly specified set of feasible options
• Find one/all/k optimal, feasible element(s)
• Applications
• Product configuration (PC, vacation)
• Optimal plan selection
• Content/display adaptation and personalization

25
Solving PCOOrdered Generate Test

• Generate outcomes in non-increasing order
• linearize the partial order over all possible
  elements
• Test for feasibility
• Check for optimality
• First feasible outcome is optimal!
• Need more?
• Maintain set of optimal solutions
• New solution is optimal is not dominated by any
  previously generated solution

26
Generating a Non-increasing Sequence of Outcomes

• Topologically sort the variables
• Build an assignment (search) tree by
  instantiating variables according to this order
• Order variable values based on the CPT
• Leaf nodes, ordered left to right ( depth-first
  traversal of the tree) correspond to a
  non-increasing sequence of outcomes

27
(No Transcript)
28
Improvements

• Use CSP pruning techniques
• Meta-constrains on CSP solution
• Branch and bound eliminate sub-tree when
• We assign a variable to a less preferred value
• Current set of constraints as strong as for some
  previous value of this variable

29
(No Transcript)
30
Anytime Behavior

• First feasible solution is optimal!
• No theoretical overhead beyond standard CSP
  solution
• No item withdrawn from set of current solutions
• To obtain more than one solution dominance
  testing required
• Can lead to considerable computational overhead

31
Applications
32
Flight Selection (Brafman, Domshlak, Kogan
UAI04)

• Instance of selecting optimal element problem
• Approach
• User supplies
• constraints (source, destination, etc.)
• initial preferences
• Preferences compiled into UCP-net
• Top k results shown
• User provides feedback
• What she likes or not
• What she would like improved
• Top results revised accordingly

33
Planning for Data Products (Golden et. al.)

• NASA collects much raw data about earth
• Requires extensive processing to be useful
• Each Earth scientists needs different processing
• ImageBot generates data plans for such products
• Data plans run scientific models, combine and
  transform data in order to achieve data goals
• Many plans can generate one data product
• Each plan has different value
• Using a simple preference language ImageBot
  planning algorithm is biased towards more
  preferred plans

34
Adaptive, Personalized Rich Media Presentations

• Presentations with diverse media elements
  requiring spatio-temporal synchronization
• Target wide audiences
• Audience members have different tastes, different
  network connections, and use different devices
• Goal provide designers with tools for designing
  presentations that adapt to user and user context

35
Example ESPN Promo

• Presentation with five elements
• Video featuring upcoming broadcast
• 2 image ads
• Video ad
• Running text with scores/news
• Each media element is a variable
• Additional variables denote user properties,
  device properties, bandwidth
• Variable values different content and quality
  options

36
How Does It Work?

• Variables denote different presentation elements
  (video, ads, running text)
• Additional variables denote context information
• TCP-nets specify preference relation over
  presentations
• Author may specify additional constraints
• At download time combine
• TCP-net
• Information about user and user context
• Resulting constrained optimization problem solved
• Output a SMIL presentation

37
CP-Net for ESPN Promo
Gender
Nationality
38
Current Issues and Projects

• Set preferences specifying and computing
  preferred subsets when items have synergy
  AAAI06
• Continuous monitoring
• An application that requires set preferences
• Browsing large heterogeneous databases
• Joint work with Scott Klemer, Ron Yeh, and Yoav
  Shoham supported by NSF

39
Collaborators

• Carmel Domshlak Technion
• All work
• Craig Boutilier University of Toronto
• CP-nets, UCP-nets
• Holger Hoos, David Poole UBC
• CP-nets
• Doron Friedman University College London
• Adaptive presentations
• Solomon Shimony Ben-Gurion University
• Adaptive presentation, TCP-nets, Set preferences

40
Summary

• Much recent interest in work on preference
  representation, elicitation, and reasoning
• xCP-nets offer a simple preference language and
  convenient graphical and algorithmic tools
• UCP-nets provide good target for knowledge
  compilation
• Many applications in e-commerce and user
  interfaces

41
(No Transcript)