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Towards a Game-Theoretic Framework for Information Retrieval ChengXiang Zhai 翟成祥 Department of Computer Science University of Illinois at Urbana-Champaign http://www.cs.uiuc.edu/homes/czhai Email: czhai@illinois.edu CCIR 2014, Aug. 10, 2014, Kunming, China 1

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Search is everywhere, and part of everyone’s life Web Search Desk Search Site Search Enterprise Search Social Media Search … 2

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Search is also important for big data: make big data small, but more useful Information Retrieval Text MiningDecision Support Big Raw Data Small Relevant Data 3

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Search accuracy matters! Sources: Google, Twitter: http://www.statisticbrain.com/http://www.statisticbrain.com/ PubMed: http://www.ncbi.nlm.nih.gov/About/tools/restable_stat_pubmed.htmlhttp://www.ncbi.nlm.nih.gov/About/tools/restable_stat_pubmed.html # Queries /Day 4,700,000,000 1,600,000,000 2,000,000 ~1,300,000 hrs X 1 secX 10 sec ~13,000,000 hrs ~440,000 hrs ~4,400,000 hrs ~550 hrs ~5,500 hrs … How can we optimize all search engines in a general way? 4

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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? How can we optimize all search engines in a general way? 5

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Current-generation search engines Document collection k number of queries search engines Query Q Ranked list Retrieval Model Minimum NLP Machine Learning D Score(Q,D) Retrieval task = rank documents for a query Interface = ranked list ( “10 blue links”) Optimal Search Engine=optimal score(q,d) Objective = ranking accuracy on training data 6

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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 7

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Two Justifications of PRP Optimization of traditional retrieval effectiveness measures –Given an expected level of recall, ranking based on PRP maximizes the precision –Given a fixed rank cutoff, ranking based on PRP maximizes precision and recall Optimal decision making –Regardless the tradeoffs (e.g., favoring high precision vs. high recall), ranking based on PRP optimizes the expected utility of a binary (independent) retrieval decision (i.e., to retrieve or not to retrieve a document) Intuition: if a user sequentially examines one doc at each time, we’d like the user to see the very best ones first 8

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Success of Probability Ranking Principle Vector Space Models: [Salton et al. 1975], [Singhal et al. 1996], … Classic Probabilistic Models: [Maron & Kuhn 1960], [Harter 1975], [Robertson & Sparck Jones 1976], [van Rijsbergen 1977], [Robertson 1977], [Robertson et al. 1981], [Robertson & Walker 1994], … Language Models: [Ponte & Croft 1998], [Hiemstra & Kraaij 1998], [Zhai & Lafferty 2001], [Lavrenko & Croft 2001], [Kurland & Lee 2004], … Non-Classic Logic Models: [van Rijsbergen 1986], [Wong & Yao 1995], … Divergence from Randomness: [Amati & van Rijsbergen 2002], [He & Ounis 2005], … Learning to Rank: [Fuhr 1989], [Gey 1994],... Axiomatic retrieval framework [Fang et al. 2004], [Fang et al. 2011], … … Most information retrieval models are to optimize score(Q,D) 9

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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 10

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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] However, scoring is still for just one query : score(Q, ) Optimal SE = optimal score(Q, ) Objective = Ranking accuracy on training data 11

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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 … 12

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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]) Can we solve all these problems in a more principled way with a unified formal framework? 13

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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? 14

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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 makes the first move; system makes the last move – 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 15

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Search as a Sequential Game UserSystem A 1 : Enter a query Which information items to present? How to present them? R i : results (i=1, 2, 3, …) Which items to view? A 2 : View item Which aspects/parts of the item to show? How? R’: Item summary/preview View more? A 3 : Scroll down or click on “Back”/”Next” button (Satisfy an information need with minimum effort) (Satisfy an information need with minimum user effort, minimum resource) 16

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Retrieval Task = Sequential Decision-Making User U: A 1 A 2 … … A t-1 A t System: R 1 R 2 … … R t-1 Given U, C, A t, and H, choose the best R t from all possible responses to A t History H={(A i,R i )} i=1, …, t-1 Info Item Collection C Query=“light laptop” All possible rankings of items in C The best ranking for the query Click on “Next” button All possible rankings of unseen items The best ranking of unseen items R t r(A t ) R t =? 17

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Formalization based on Bayesian Decision Theory : Risk Minimization Framework [Zhai & Lafferty 06, Shen et al. 05] User: U Interaction history: H Current user action: A t Document collection: C Observed All possible responses: r(A t )={r 1, …, r n } User Model M=(S, U,… ) Seen items Information need L(r i,A t,M)Loss Function Optimal response: r* (minimum loss) ObservedInferred Bayes risk 18

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Approximate the Bayes risk by the loss at the mode of the posterior distribution 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 A Simplified Two-Step Decision-Making Procedure 19

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Optimal Interactive Retrieval User A1A1 UC M* 1 P(M 1 |U,H,A 1,C) L(r,A 1,M* 1 ) R1R1 A2A2 L(r,A 2,M* 2 ) R2R2 M* 2 P(M 2 |U,H,A 2,C) A3A3 … Collection IR system Many possible actions: -type in a query character - scroll down a page - click on any button -… Many possible responses: -query completion -display adaptive summaries -recommendation/advertising -clarification -… M can be regarded as states in an MDP or POMDP. Thus reinforcement learning will be very useful! (see SIGIR’14 tutorial on dynamic IR modeling [Yang et al. 14]) 20

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Refinement of Risk Minimization Framework r(A t ): decision space (A t dependent) – r(A t ) = all possible rankings of items in C – r(A t ) = all possible rankings of unseen items – r(A t ) = all possible summarization strategies – r(A t ) = all possible ways to diversify top-ranked items – r(A t ) = all possible ways to mix results with query suggestions (or topic map) M: user model – Essential component: U = user information need – S = seen items – n = “new topic?” (or “Never purchased such a product before”?) – t = user’s task? L(R t,A t,M): loss function – Generally measures the utility of R t 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, A t, 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) 21

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Case 1: Context-Insensitive IR – A t =“enter a query Q” – r(A t ) = all possible rankings of docs in C – M= U, unigram language model (word distribution) – p(M|U,H,At,C)=p( U |Q) 22

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Optimal Ranking for Independent Loss Decision space = {rankings} Sequential browsing Independent loss Independent risk = independent scoring “Risk ranking principle” [Zhai 02, Zhai & Lafferty 06] 23

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Case 2: Implicit Feedback – A t =“enter a query Q” – r(A t ) = 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) 24

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Case 3: General Implicit Feedback – A t =“enter a query Q” or “Back” button, “Next” button – r(A t ) = 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) 25

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Case 4: User-Specific Result Summary – A t =“enter a query Q” – r(A t ) = {(D, )}, D C, |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*) n*=1n*=0 i =snippet 10 i =overview 01 Choose k most relevant docs If a new topic (n*=1), give an overview summary; otherwise, a regular snippet summary 26

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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 27

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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] 28

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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: A 1 : spot-welding robotics A 2 : controlling inventory A 3 : pipe-laying robots A 4 : talking robot A 5 : robots for loading & unloading memory tapes A 6 : robot [telephone] operators A 7 : robot cranes … Subtopic judgments A 1 A 2 A 3 …... A k d 1 1 1 0 0 … 0 0 d 2 0 1 1 1 … 0 0 d 3 0 0 0 0 … 1 0 …. d k 1 0 1 0... 0 1 This is a non-traditional retrieval task … 29

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5.1 Diversify = Remove Redundancy “Willingness to tolerate redundancy” C2

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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 31

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Aspect Loss Function: Illustration Desired coverage p(a| Q ) “Already covered” p(a| 1 )... p(a| k -1 ) Combined coverage p(a| k ) New candidate p(a| k ) non-relevant redundant perfect 32

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5.3 Diversify = Active Feedback [Shen & Zhai 05] Decision problem: Decide subset of documents for relevance judgment 33

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Independent Loss 34

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Independent Loss (cont.) Uncertainty Sampling Top K 35

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Dependent Loss Heuristics: consider relevance first, then diversity Gapped Top K Select Top N documents Cluster N docs into K clusters K Cluster Centroid MMR … 36

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Illustration of Three AF Methods Top-K (normal feedback) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 … Gapped Top-K K-cluster centroid Experiment results show that Top-K is worse than all others [Shen & Zhai 05] 37

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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 –... 38

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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) 39

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An interesting new problem: Crowdsourcing to users for relevance judgments collection Assumption: Approximate relevance judgments with clickthroughs Question: how to optimize the exploration- exploitation tradeoff when leveraging users to collect clicks on lowly-ranked (“tail”) documents? – Where to insert a candidate ? – Which user should get this “assignment”? Potential solution must include a model for a user’s behavior 40

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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? 41

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Some Relevant Challenges in NLP How can we turn partial understanding into additional dimension of scoring ? – Readability – Trustworthiness 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? 42

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Intelligent IR System in the Future: Optimizing multiple games simultaneously Game 1 Game 2 Game k Log Intelligent IR System Documents – 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 Learning engine (MOOC) Mobile service search Medical advisor 43

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Action Item: future research requires integration of multiple fields Document Collection Document Understanding User Understanding Interactive Service (Search, Browsing, Recommend…) User action System response User Model Document Representation User interaction Log External Doc Info (structures) External User Info (social network) Natural Language Processing Machine Learning (particularly reinforcement learning) Game Theory (Economics) Human-Computer Interaction Traditional Information Retrieval Psychology 44

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References [Salton et al. 1975] A theory of term importance in automatic text analysis. G. Salton, C.S. Yang and C. T. Yu. Journal of the American Society for Information Science, 1975. [Singhal et al. 1996] Pivoted document length normalization. A. Singhal, C. Buckley and M. Mitra. SIGIR 1996. [Maron&Kuhn 1960] On relevance, probabilistic indexing and information retrieval. M. E. Maron and J. L. Kuhns. Journal o fhte ACM, 1960. [Harter 1975] A probabilistic approach to automatic keyword indexing. S. P. Harter. Journal of the American Society for Information Science, 1975. [Robertson&Sparck Jones 1976] Relevance weighting of search terms. S. Robertson and K. Sparck Jones. Journal of the American Society for Information Science, 1976. [van Rijsbergen 1977] A theoretical basis for the use of co-occurrence data in information retrieval. C. J. van Rijbergen. Journal of Documentation, 1977. [Robertson 1977] The probability ranking principle in IR. S. E. Robertson. Journal of Documentation, 1977. 45 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.czhai@illinois.edu

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References (cont.) [Robertson 1981] Probabilistic models of indexing and searching. S. E. Robertson, C. J. van Rijsbergen and M. F. Porter. Information Retrieval Search, 1981. [Robertson&Walker 1994] Some simple effective approximations to the 2-Poisson model for probabilistic weighted retrieval. S. E. Robertson and S. Walker. SIGIR 1994. [Ponte&Croft 1998] A language modeling approach to information retrieval. J. Ponte and W. B. Croft. SIGIR 1998. [Hiemstra&Kraaij 1998] Twenty-one at TREC-7: ad-hoc and cross-language track. D. Hiemstra and W. Kraaij. TREC-7. 1998. [Zhai&Lafferty 2001] A study of smoothing methods for language models applied to ad hoc information retrieval. C. Zhai and J. Lafferty. SIGIR 2001. [Lavrenko&Croft 2001] Relevance-based language models. V. Lavrenko and B. Croft. SIGIR 2001. [Kurland&Lee 2004] Corpus structure, language models, and ad hoc information retrieval. O. Kurland and L. Lee. SIGIR 2004. [van Rijsbergen 1986] A non-classical logic for information retrieval. C. J. van Rijsbergen. The Computer Journal, 1986. [Wong&Yao 1995] On modeling information retrieval with probabilistic inference. S. K. M. Wong and Y. Y. Yao. ACM Transactions on Information Systems. 1995. 46

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References (cont.) [Amati&van Rijsbergen 2002] Probabilistic models of information retrieval based on measuring the divergence from randomness. G. Amati and C. J. van Rijsbergen. ACM Transactions on Information Retrieval. 2002. [He&Ounis 2005] A study of the dirichlet priors for term frequency normalization. B. He and I. Ounis. SIGIR 2005. [Fuhr 89] Norbert Fuhr: Optimal Polynomial Retrieval Functions Based on the Probability Ranking Principle. ACM Trans. Inf. Syst. 7(3): 183-204 (1989) [Gey 1994] Inferring probability of relevance using the method of logistic regression. F. Gey. SIGIR 1994. [Fang et al. 2004] H. Fang, T. Tao, C. Zhai, A formal study of information retrieval heuristics. SIGIR 2004. [Fang et al. 2011] H. Fang, T. Tao, C. Zhai, Diagnostic evaluation of information retrieval models, ACM Transactions on Information Systems, 29(2), 2011 [Zhai & Lafferty 06] ChengXiang Zhai, John D. Lafferty: A risk minimization framework for information retrieval. Inf. Process. Manage. 42(1): 31-55 (2006) [Zhai 02] ChengXiang Zhai, Risk Minimization and Language Modeling in Information Retrieval, Ph.D. thesis, Carnegie Mellon University, 2002. [Cao et al. 07] Zhe Cao, Tao Qin, Tie-Yan Liu, Ming-Feng Tsai, and Hang Li. 2007. Learning to rank: from pairwise approach to listwise approach. In Proceedings of the 24th international conference on Machine learning (ICML '07), pp.129-136, 2007 47

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References (cont.) [Shen et al. 05] Xuehua Shen, Bin Tan, and ChengXiang Zhai, Implicit User Modeling for Personalized Search, In Proceedings of the 14th ACM International Conference on Information and Knowledge Management ( CIKM'05), pages 824-831. [Zhai et al. 03] ChengXiang Zhai, William W. Cohen, and John Lafferty, Beyond Independent Relevance: Methods and Evaluation Metrics for Subtopic Retrieval, Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval ( SIGIR'03 ), pages 10-17, 2003. [Shen & Zhai 05] Xuehua Shen, ChengXiang Zhai, Active Feedback in Ad Hoc Information Retrieval, Proceedings of the 28th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval ( SIGIR'05), 59-66, 2005. [Teevan et al. 10] Jaime Teevan, Susan T. Dumais, Eric Horvitz: Potential for personalization. ACM Trans. Comput.-Hum. Interact. 17(1) (2010) [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. 48

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References (cont.) [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/dynamic- information-retrieval-tutorialhttp://www.slideshare.net/marcCsloan/dynamic- information-retrieval-tutorial 49

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Thank You! Questions/Comments? 50

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