Towards a Game-Theoretic Framework for Information Retrieval ChengXiang (“Cheng”) Zhai Department of Computer Science University of Illinois at Urbana-Champaign http://www.cs.uiuc.edu/homes/czhai Email: czhai@illinois.edu Yahoo!-DAIS Seminar, UIUC, Jan 23, 2015 1 Search is everywhere, and part of everyone’s life Web Search Desk Search Enterprise Search Social Media Search Site Search …… 2 Search accuracy matters! # Queries /Day X 1 sec X 10 sec 4,700,000,000 ~1,300,000 hrs ~13,000,000 hrs 1,600,000,000 ~440,000 hrs ~4,400,000 hrs 3,000,000 …… ~550 hrs ~5,500 hrs How can we optimize all search engines in a general way? Sources: Google: http://www.statisticbrain.com/google-searches/ Twitter: http://www.statisticbrain.com/twitter-statistics/ PubMed: http://www.nlm.nih.gov/services/pubmed_searches.html 3 How can we optimize all search engines in a general way? However, this is an ill-defined question! What is a search engine? What is an optimal search engine? What should be the objective function to optimize? 4 Current-generation search engines number of queries k search engines Document collection Query Q Retrieval task = rank documents for a query Interface = ranked list ( “10 blue links”) Ranked list Score(Q,D) Optimal Search Engine=optimal score(q,d) D Machine Learning Retrieval Model Objective = ranking accuracy on training data Minimum NLP 5 Current search engines are well justified • Probability ranking principle [Robertson 77]:returning a ranked list of documents in descending order of probability that a document is relevant to the query is the optimal strategy under two assumptions: – The utility of a document (to a user) is independent of the utility of any other document – A user would browse the results sequentially • Intuition: if a user sequentially examines one doc at each time, we’d like the user to see the very best ones first 6 Success of Probability Ranking Principle • Vector Space Models: [Salton et al. 75], [Singhal et al. 96], … • Classic Probabilistic Models: [Maron & Kuhn 60], [Harter 75], [Robertson & Sparck Jones 76], [van Rijsbergen 77], [Robertson 77], [Robertson et al. 81], [Robertson & Walker 94], … • Language Models: [Ponte & Croft 98], [Hiemstra & Kraaij 98], [Zhai & Lafferty 01], [Lavrenko & Croft 01], [Kurland & Lee 04], … • Non-Classic Logic Models: [van Rijsbergen 86], [Wong & Yao 95], … • Divergence from Randomness: [Amati & van Rijsbergen 02], [He & Ounis 05], … • Learning to Rank: [Fuhr 89], [Gey 94], ... • Axiomatic retrieval framework [Fang et al. 04], [Clinchant & Gaussier 10], [Fang et al. 11], … • … Most information retrieval models are to optimize score(Q,D) 7 Limitations of PRP Limitations of optimizing Score(Q,D) • Assumptions made by PRP don’t hold in practice – Utility of a document depends on others – Users don’t strictly follow sequential browsing • As a result – Redundancy can’t be handled (duplicated docs have the same score!) – Collective relevance can’t be modeled – Heuristic post-processing of search results is inevitable 8 Improvement: instead of scoring one document, score a whole ranked list • Instead of scoring an individual document, score an entire candidate ranked list of documents [Zhai 02; Zhai & Lafferty 06] – A list with redundant documents on the top can be penalized – Collective relevance can be captured also – Powerful machine learning techniques can be used [Cao et al. 07] • PRP extended to address interaction of users [Fuhr 08] • However, scoring is still for just one query: score(Q, ) Optimal SE = optimal score(Q, ) Objective = Ranking accuracy on training data 9 Limitations of single query scoring • • • • No consideration of past queries and history No modeling of users Can’t optimize the utility over an entire session … 10 Heuristic solutions emerging topics in IR • No consideration of past queries and history Implicit feedback (e.g, [Shen et al. 05] ), personalized search (see, e.g., [Teevan et al. 10]) • No modeling of users intent modeling (see, e.g. , [Shen et al. 06]), task inference (see, e.g., [Wang et al. 13]) • Can’t optimize the utility over an entire session Active feedback (e.g., [Shen & Zhai 05]), exploration-exploitation tradeoff (e.g., [Agarwal et al. 09], [Karimzadehgan & Zhai 13]) POMDP for session search [Luo et al. 14] Can we solve all these problems in a more principled way with a unified formal framework? 11 Going back to the basic questions… • • • • What is a search engine? What is an optimal search engine? What should be the objective function to optimize? How can we solve such an optimization problem? 12 Proposed Solution: A Game-Theoretic Framework for IR • Retrieval process = cooperative game-playing • Players: Player 1= search engine; Player 2= user • Rules of game: – – – – – Each player takes turns to make “moves” User or system (in case of recommender system) makes the first move User makes the last move (usually) For each move of the user, the system makes a response move Current search engine: • User’s moves= {query, click}; system’s moves = {ranked list, show doc} • Objective: multiple possibilities – satisfying the user’s information need with minimum effort of user and minimum resource overhead of the system. – Given a constant effort of a user, subject to constraints of system resources, maximize the utility of delivered information to the user – Given a fixed “budget” for system resources, and an upper bound of user effort, maximize the utility of delivered information 13 Search as a Sequential Game (Satisfy an information need with minimum effort) User A1 : Enter a query Which items to view? A2 : View item View more? (Satisfy an information need with minimum user effort, minimum resource) System Which information items to present? How to present them? Ri: results (i=1, 2, 3, …) Which aspects/parts of the item to show? How? R’: Item summary/preview A3 : Scroll down or click on “Back”/”Next” button 14 Retrieval Task = Sequential Decision-Making History H={(Ai,Ri)} i=1, …, t-1 Given U, C, At , and H, choose the best Rt from all possible responses to At Query=“light laptop” User U: System: A1 A2 … … At-1 R1 R2 … … Rt-1 C Info Item Collection Click on “Next” button At Rt =? The best ranking for the query The best ranking of unseen items Rt r(At) All possible rankings of items in C All possible rankings of unseen items 15 Formalization based on Bayesian Decision Theory : Risk Minimization Framework [Zhai & Lafferty 06, Shen et al. 05] Observed User Model User: U Interaction history: H Current user action: At Document collection: C Seen items M=(S, U,… ) Information need All possible responses: r(At)={r1, …, rn} L(ri,At,M) Loss Function Optimal response: r* (minimum loss) Rt arg min rr ( At ) L(r , At , M ) P( M | U , H , At , C )dM M Bayes risk Inferred Observed 16 A Simplified Two-Step Decision-Making Procedure • Approximate the Bayes risk by the loss at the mode of the posterior distribution Rt arg min rr ( At ) L(r , At , M ) P( M | U , H , At , C )dM M arg min rr ( At ) L(r , At , M *) P( M * | U , H , At , C ) arg min rr ( At ) L(r , At , M *) where M * arg max M P( M | U , H , At , C ) • Two-step procedure – Step 1: Compute an updated user model M* based on the currently available information – Step 2: Given M*, choose a response to minimize the loss function 17 Optimal Interactive Retrieval User A1 Many possible actions: -type in a query character - scroll down a page A - click on any 2button -… U M*1 C Collection P(M1|U,H,A1,C) Many possible responses: L(r,A1,M*1) -query completion R1 -display adaptive summaries -recommendation/advertising -clarification M*2 P(M2|U,H,A -…2,C) L(r,A2,M*2) … * M (user model) can be regarded as states in an MDP or POMDP. R2 A3 Thus reinforcement learning willIR be useful system (see SIGIR’14 tutorial on dynamic IR modeling [Yang et al. 14]) * Interaction can be modeled at different levels: keyboard input, result clicking , and query formulations, multisession tasks, … 18 Refinement of Risk Minimization Framework • r(At): decision space (At dependent) – – – – – r(At) = all possible rankings of items in C r(At) = all possible rankings of unseen items r(At) = all possible summarization strategies r(At) = all possible ways to diversify top-ranked items r(At) = all possible ways to mix results with query suggestions (or topic map) – – – – Essential component: U = user information need S = seen items n = “new topic?” (or “Never purchased such a product before”?) t = user’s task? • M: user model • L(Rt ,At,M): loss function – Generally measures the utility of Rt for a user modeled as M – Often encodes relevance criteria, but may also capture other preferences – Can be based on long-term gain (i.e., “winning the whole “game” of info service) • P(M|U, H, At, C): user model inference – Often involves estimating the information need U – May involve inference of other variables also (e.g., task, exploratory vs. fixed item search) 19 Case 1: Context-Insensitive IR – – – – At=“enter a query Q” r(At) = all possible rankings of docs in C M= U, unigram language model (word distribution) p(M|U,H,At,C)=p(U |Q) L(ri , At , M ) L((d1 ,..., d N ), U ) N p (viewed | d i )D (U || di ) i 1 Since p (viewed | d1 ) p (viewed | d 2 ) .... the optimal ranking Rt is given by ranking documents by D (U || di ) 20 Optimal Ranking for Independent Loss * arg min L( , ) p( | q,U , C, S )d N i i 1 j 1 N i L( , ) si l ( j |1... j 1 ) si l ( j ) i 1 j 1 N N j 1 j 1 i 1 ( N * arg min ( j 1 Sequential browsing Independent loss si )l ( j ) N j 1 i 1 N N j 1 j 1 i 1 arg min ( Decision space = {rankings} si )l ( j ) p( | q, U , C , S ) d si ) l ( j ) p( j | q, U , C , S )d j r (d k | q, U , C , S ) l ( k ) p ( k | q, U , C , S )d k Independent risk = independent scoring * Ranking based on r (d k | q,U , C , S ) “Risk ranking principle” [Zhai 02, Zhai & Lafferty 06] 21 Case 2: Implicit Feedback – – – – – At=“enter a query Q” r(At) = all possible rankings of docs in C M= U, unigram language model (word distribution) H={previous queries} + {viewed snippets} p(M|U,H,At,C)=p(U |Q,H) L(ri , At , M ) L((d1 ,..., d N ), U ) N p (viewed | d i )D (U || di ) i 1 Since p (viewed | d1 ) p (viewed | d 2 ) .... the optimal ranking Rt is given by ranking documents by D (U || di ) 22 Case 3: General Implicit Feedback – – – – – At=“enter a query Q” or “Back” button, “Next” button r(At) = all possible rankings of unseen docs in C M= (U, S), S= seen documents H={previous queries} + {viewed snippets} p(M|U,H,At,C)=p(U |Q,H) L(ri , At , M ) L((d1 ,..., d N ), U ) N p (viewed | d i )D (U || di ) i 1 Since p (viewed | d1 ) p (viewed | d 2 ) .... the optimal ranking Rt is given by ranking documents by D (U || di ) 23 Case 4: User-Specific Result Summary – – – – At=“enter a query Q” r(At) = {(D,)}, DC, |D|=k, {“snippet”,”overview”} M= (U, n), n{0,1} “topic is new to the user” p(M|U,H,At,C)=p(U, n|Q,H), M*=(*, n*) L( i , n*) L(ri , At , M ) L( Di , i , *, n*) n*=1 n*=0 L( Di , *) L( i , n*) D( * || d Di Choose k most relevant docs d ) L( i , n*) i=snippet i=overview 1 0 0 1 If a new topic (n*=1), give an overview summary; otherwise, a regular snippet summary 24 Case 5: Modeling Different Notions of Diversification • Redundancy reduction reduce user effort • Diverse information needs (e.g., overview, subtopic retrieval) increase the immediate utility • Active relevance feedback increase future utility 25 Risk Minimization for Diversification • Redundancy reduction: Loss function includes a redundancy measure – Special case: list presentation + MMR [Zhai et al. 03] • Diverse information needs: loss function defined on latent topics – Special case: PLSA/LDA + topic retrieval [Zhai 02] • Active relevance feedback: loss function considers both relevance and benefit for feedback – Special case: hard queries + feedback only [Shen & Zhai 05] 26 Subtopic Retrieval [Zhai et al. 03] Query: What are the applications of robotics in the world today? Find as many DIFFERENT applications as possible. Example subtopics: A1: spot-welding robotics A2: controlling inventory A3: pipe-laying robots A4: talking robot A5: robots for loading & unloading memory tapes A6: robot [telephone] operators A7: robot cranes …… Subtopic judgments d1 d2 d3 …. dk A1 A2 A3 … ... Ak 1 1 0 0… 0 0 0 1 1 1… 0 0 0 0 0 0… 1 0 1 0 1 0 ... 0 1 This is a non-traditional retrieval task … 27 5.1 Diversify = Remove Redundancy N N * arg min L( , ) p( | q, U , C , S )d arg min si r (d j | d1 ,..., d j1 ) j 1 i j r (d k | d1 ,..., d k 1 ) r (d k | d1 ,..., d k 1 , ) p ( | q, U , C , S )d Greedy Algorithm for Ranking: Maximal Marginal Relevance (MMR) l (d k | d1 ,..., d k 1 , Q , { i }ik11 ) c2 p(Re l | d k )(1 p ( New | d k )) c3 (1 p (Re l | d k )) Cost REL NON-REL NEW 0 C3 where, NOT-NEW C2 C3 c3 1 c2 Rank Rank p(Re l | d k )(1 p( New | d k )) p(q | d k ) (1 p( New | d k )) “Willingness to tolerate redundancy” C2<C3, since a redundant relevant doc is better than a non-relevant doc 28 5.2 Diversity = Satisfy Diverse Info. Need [Zhai 02] • Need to directly model latent aspects and then optimize results based on aspect/topic matching • Reducing redundancy doesn’t ensure complete coverage of diverse aspects 29 Aspect Loss Function: Illustration perfect redundant Desired coverage“Already covered” p(a|Q) p(a|1)... p(a|k -1) non-relevant New candidate p(a|k) Combined coverage p(a|k) 30 5.3 Diversify = Active Feedback [Shen & Zhai 05] Decision problem: Decide subset of documents for relevance judgment D arg min L( D, ) p( | U , q, C)d * D L ( D, ) l ( D , j , ) p ( j | D , , U ) j k l ( D, j , ) p ( ji | di , ,U ) j i 1 31 Independent Loss k L( D, ) l ( D, j , ) p( ji | di , , U ) i 1 j Independent Loss k l ( D, j, ) l (di , ji , ) k k L( D, ) l (di , ji , ) p( ji | d i , ,U ) i 1 i 1 j i 1 k D* arg min l (di , ji , ) p( ji | di , ,U ) p( | U , q, C )d D i 1 ji r (di ) l (di , ji , ) p( ji | di , ,U ) p( | U , q, C )d ji 32 Independent Loss (cont.) r (di ) l (d i , ji , ) p ( ji | d i , , U ) p ( | U , q, C ) d ji di C , l (di ,1, ) C1 , l (di , 0, ) C0 , C1 C0 l (di ,1, ) log p( R 1| di , ) di C l (di ,0, ) log p( R 0 | di , ) di C r (di ) C0 (C1 C0 ) p( ji 1| di , ,U ) p( | U , q, C )d Top K r (di ) H ( R | di , ) p( | U , q, C )d Uncertainty Sampling 33 Dependent Loss k L( D,U , ) p( ji 1| di , ,U ) ( D, ) i 1 Heuristics: consider relevance first, then diversity Select Top N documents … N (G 1) K Cluster N docs into K clusters K Cluster Centroid Gapped Top K MMR 34 Illustration of Three AF Methods Gapped Top-K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 … Top-K (normal feedback) K-cluster centroid Experiment results show that Top-K is worse than all others [Shen & Zhai 05] 35 Suggested answers to the basic questions • Search Engine = Game System • Optimal Search Engine = Optimal Game Plan/Strategy • Objective function: based on 3 factors and at the session level – Utility of information delivered to the user – Effort needed from the user – System resource overhead • How can we solve such an optimization problem? – Bayesian decision theory in general, partially observable Markov decision process (POMDP) [Luo et al. 14] – Reinforcement learning – ... 36 Major benefits of IR as game playing • Naturally optimize performance on an entire session instead of that on a single query (optimizing the chance of winning the entire game) • It optimizes the collaboration of machines and users (maximizing collective intelligence) • It opens up many interesting new research directions (e.g., crowdsourcing + interactive IR) 37 An interesting new problem: Crowdsourcing to users for relevance judgments collection • Assumption: Approximate relevance judgments with clickthroughs • Question: how to optimize the explorationexploitation tradeoff when leveraging users to collect clicks on lowly-ranked (“tail”) documents? – Where to insert a candidate ? – Which user should get this “assignment” and when? • Potential solution must include a model for a user’s behavior 38 General Research Questions Suggested by the Game-Theoretic Framework • How should we design an IR game? – How to design “moves” for the user and the system? – How to design the objective of the game? – How to go beyond search to support access and task completion? • How to formally define the optimization problem and compute the optimal strategy for the IR system? – To what extent can we directly apply existing game theory? Does Nash equilibrium matter? – What new challenges must be solved? • How to evaluate such a system? MOOC? 39 A few specific questions • How can we support natural interaction via “explanatory feedback”? – I want documents similar to this one except for not matching “X” – I want documents similar to this one, but also further matching “Y” – … • How can we model a user’s non-topical preferences? – Readability – Freshness – … • • • • • How can we perform syntactic and semantic analysis of queries? How can we generate adaptive explanatory summaries of documents? How can we generate coherent preview of search results ? How can we generate a topic map to enable users to browse freely? … 40 Intelligent IR System in the Future: Optimizing multiple games simultaneously Game 2 Game 1 Learning engine (MOOC) Mobile service search Intelligent IR System Game k Medical advisor –Support whole workflow of a user’s task (multimodel info access, info analysis, decision support, task support) –Minimize user effort (maximum relevance, natural dialogue) –Minimize system resource overhead –Learn to adapt & improve over time from all users/data Log Documents 41 Action Item: future research requires integration of multiple fields Psychology User action Human-Computer Interactive Service Game Theory (Economics) (Search, Browsing, Recommend…) Interaction System response Document Collection Traditional Information Retrieval User Understanding User Model Natural Language Processing Document Representation Document Understanding Natural Language Processing Machine Learning (particularly reinforcement learning) External User External Doc User interaction Log Info (social network) Info (structures) 42 References Note: the references are inevitably incomplete due to the breadth of the topic; if you know of any important missing references, please email me at czhai@illinois.edu. • • • • • • • [Salton et al. 1975] A theory of term importance in automatic text analysis. 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Interact. 17(1) (2010) 46 References (cont.) • • • • • • [Shen et al. 06] Dou Shen, Jian-Tao Sun, Qiang Yang, and Zheng Chen. 2006. Building bridges for web query classification. In Proceedings of the 29th annual international ACM SIGIR 2006, pp. 131-138. [Wang et al. 13] Hongning Wang, Yang Song, Ming-Wei Chang, Xiaodong He, Ryen W. White, and Wei Chu. 2013. Learning to extract cross-session search tasks, WWW’ 2013. 1353-1364. [Agarwal et al. 09] Deepak Agarwal, Bee-Chung Chen, and Pradheep Elango. 2009. Explore/Exploit Schemes for Web Content Optimization. In Proceedings of the 2009 Ninth IEEE International Conference on Data Mining (ICDM '09), 2009. [Karimzadehgan & Zhai 13] Maryam Karimzadehgan, ChengXiang Zhai. A Learning Approach to Optimizing Exploration-Exploitation Tradeoff in Relevance Feedback, Information Retrieval , 16(3), 307-330, 2013. [Luo et al. 14] J. Luo, S. Zhang, G. H. Yang, Win-Win Search: Dual-Agent Stochastic Game in Session Search. ACM SIGIR 2014. [Yang et al. 14] G. H. Yang, M. Sloan, J. Wang, Dynamic Information Retrieval Modeling, ACM SIGIR 2014 Tutorial; http://www.slideshare.net/marcCsloan/dynamicinformation-retrieval-tutorial 47 Thank You! Questions/Comments? 48