On the Equilibrium of Query Reformulation and Document Retrieval
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In this paper, we study the interactions between query reformulation and retrieval model relevance estimation in a game theoretical framework. Under the proposed strategic game of information retrieval (IR), a query formulator, as one of the players, taking actions to produce the optimal query, is expected to maximize its own utility with respect to the relevance estimation of documents produced by the other player, a retrieval modeler; simultaneously, the retrieval modeler, taking actions to produce the document relevance scores, needs to optimize its likelihood from the training data with respect to the refined query produced by the query formulator. Their equilibrium or equilibria will be reached when both are the best response to each other. We derive our equilibrium theory of IR using normal-form representations: when a standard relevance feedback algorithm is coupled with a retrieval model, they share the same objective function and thus would form a partnership game; by contrast, pseudo relevance feedback pursues a rather different objective than that of retrieval models, therefore the interactions between them would lead to a general-sum game (though implicitly collaborative). Our game theoretical analyses not only yield useful insights into the two major aspects of IR, but also offer new practical algorithms for achieving the equilibrium state of retrieval which have been shown to bring consistent performance improvements in both text retrieval and item recommendation applications.
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