Learning Strategies in Game- Theoretic Data Interaction Ben - PowerPoint PPT Presentation

Learning Strategies in Game- Theoretic Data Interaction Ben McCamish, Arash Termehchy, Behrouz Touri, Liang Huang I nformation & D ata Manag e ment and A nalytics Laboratory (IDEA) 1

Querying a database of student grades Grades First_Name Last_Name Dept. Grade … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results A user’s intent is the content they • First_Name Last_Name Dept. Grade wish to find in the database They use queries attempting to • communicate their intent 2

Most users cannot precisely express their intents Grades First_Name Last_Name Dept. Grade … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results Intent: user looking for grade of • student Kerry Smith First_Name Last_Name Dept. Grade Not sufficiently familiar with the • database content and structure 3

Most users cannot precisely express their intents Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results Query: Has last name “Smith” • First_Name Last_Name Dept. Grade Does not precisely express intent • 4

Most users cannot precisely express their intents Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database has too many tuples • matching query, mostly non-relevant. 5

Most users cannot precisely express their intents Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database system returns only a • Sarah Smith CE A subset of matching tuples John Smith EE B 6

Most users cannot precisely express their intents Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade The user doesn’t find the student • she is looking for Sarah Smith CE A John Smith EE B 7 7

Users learn by interacting with database systems Grades First_Name Last_Name Dept. Grade Smith CS … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results Reformulates query after learning about the • database and it’s content. First_Name Last_Name Dept. Grade Reformulated Query: Has last name • “Smith” and is in the Department “CS” New query expresses user’s intent much • more accurately 8

But they learn by interacting with database systems Grades First_Name Last_Name Dept. Grade Smith CS … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database system finds the desired • tuple 9

But they learn by interacting with database systems Grades First_Name Last_Name Dept. Grade Smith CS … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database system returns the • desired tuple Kerry Smith CS D 10

But they learn by interacting with database systems Grades First_Name Last_Name Dept. Grade Smith CS … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results User selects the returned tuple • First_Name Last_Name Dept. Grade Learning and reformulating query • Kerry Smith CS D allowed the user to find the desired student 11 11

Database system can learn as well Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Intent: User looking for grade of • Results student Kerry Smith First_Name Last_Name Dept. Grade Query: Has Last Name “Smith” • Does not precisely express intent • 12

Database system can learn as well Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database has too many tuples • matching query 13

Database system can learn as well Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade Database system has learned to • return Kerry Smith in CS Kerry Smith CS D department 14

Database system can learn as well Grades First_Name Last_Name Dept. Grade Smith … … … … Sarah Smith CE A John Smith EE B Kerry Smith CS D … … … … Results First_Name Last_Name Dept. Grade The user finds and selects the tuple • Kerry Smith CS D 15 15

Interaction is a game between two potentially rational agents • Two Players: user and database system • They have common interests and work together • Want to reach a mutual understanding such that user gets desired information • Strategy of the user is how intents are expressed using queries • Strategy of the database system is how to decode queries 16

User strategy User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Grades q 1 “Smith CE” First_Name Last_Name Dept. Grade q 2 “Smith” … … … … Sarah Smith CE A • Row-stochastic mapping John Smith EE B from intents to queries. Kerry Smith CS D … … … … 17

User may use a single query for multiple intents User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Grades q 1 “Smith CE” First_Name Last_Name Dept. Grade q 2 “Smith” … … … … Due to the lack of knowledge, • Sarah Smith CE A saving time, … John Smith EE B Kerry Smith CS D Makes it hard to interpret the • … … … … exact intent behind the query. 18

Database system strategy Intent # Intent Database Strategy (D) Sarah Smith e 1 ans(y) ← Grades(x,’Smith’, ‘EE’, y) e 1 e 2 e 3 in CE e 2 ans(y) ← Grades(x,’Smith’, ‘CE’, y) q 1 0 1 0 q 2 0.5 0 0.5 e 3 ans(y) ← Grades(x,’Smith’, ‘CS’, y) Query # Query Grades q 1 “Smith CE” First_Name Last_Name Dept. Grade q 2 “Smith” … … … … Sarah Smith CE A Row-stochastic mapping • John Smith EE B from queries to intents Kerry Smith CS D … … … … 19

Payoff: expected effectiveness of communicating every intent User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Database Strategy (D) q 1 “Smith CE” e 1 e 2 e 3 q 2 “Smith” q 1 0 1 0 q 2 0.5 0 0.5 Prior probability of intent • m n o X X X r ( U, D ) = D j ` prec ( e i , e ` ) U ij π i i =1 j =1 ` =1 20

Payoff: expected effectiveness of communicating every intent User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Database Strategy (D) q 1 “Smith CE” e 1 e 2 e 3 q 2 “Smith” q 1 0 1 0 q 2 0.5 0 0.5 m n o X X X r ( U, D ) = D j ` prec ( e i , e ` ) U ij π i i =1 j =1 ` =1 21

Payoff: expected effectiveness of communicating every intent User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Database Strategy (D) q 1 “Smith CE” e 1 e 2 e 3 q 2 “Smith” q 1 0 1 0 q 2 0.5 0 0.5 m n o X X X r ( U, D ) = D j ` prec ( e i , e ` ) U ij π i i =1 j =1 ` =1 22

Payoff: expected effectiveness of communicating every intent User Strategy (U) Intent # Intent q 1 q 2 e 1 John Smith in EE e 1 0 1 e 2 Sarah Smith in CE e 2 1 0 e 3 Kerry Smith in CS e 3 0 1 Query # Query Database Strategy (D) q 1 “Smith CE” e 1 e 2 e 3 q 2 “Smith” q 1 0 1 0 q 2 0.5 0 0.5 m n o X X X r ( U, D ) = D j ` prec ( e i , e ` ) U ij π i i =1 j =1 ` =1 Precision is the fraction of the returned tuples that are desired • Computed using user feedback • 23

Interesting problems 1. What are the stable states (equilibria) of the game? Is there any undesirable (sub-optimal) equilibria? 2. What are the user’s learning mechanisms? 3. What learning algorithms should the database system adopt so the collaboration converges to desirable equilibria? 1.Learning may not converge or converge to a desired equilibrium in games, e.g., Shapely game . 24

Equilibria of the game • Nash Equilibrium: A strategy profile in which no player can increase its payoff by unilaterally deviating from the current strategy Intent # Intent User Strategy (U) e 1 John Smith in EE Database Strategy (D) q 1 q 2 e 2 Sarah Smith in CE e 1 e 2 e 3 e 1 0 1 e 3 q 1 Kerry Smith in CS 0 1 0 e 2 1 0 q 2 0.5 0 0.5 e 3 0 1 Query # Query r(U,D) = 2 q 1 “Smith CE” q 2 “Smith” 25