  This paper provides a unified account of two schools of thinking in
information retrieval modelling: the generative retrieval focusing on
predicting relevant documents given a query, and the discriminative retrieval
focusing on predicting relevancy given a query-document pair. We propose a game
theoretical minimax game to iteratively optimise both models. On one hand, the
discriminative model, aiming to mine signals from labelled and unlabelled data,
provides guidance to train the generative model towards fitting the underlying
relevance distribution over documents given the query. On the other hand, the
generative model, acting as an attacker to the current discriminative model,
generates difficult examples for the discriminative model in an adversarial way
by minimising its discrimination objective. With the competition between these
two models, we show that the unified framework takes advantage of both schools
of thinking: (i) the generative model learns to fit the relevance distribution
over documents via the signals from the discriminative model, and (ii) the
discriminative model is able to exploit the unlabelled data selected by the
generative model to achieve a better estimation for document ranking. Our
experimental results have demonstrated significant performance gains as much as
23.96% on Precision@5 and 15.50% on MAP over strong baselines in a variety of
applications including web search, item recommendation, and question answering.
