User modeling in advertising and recommendation has typically focused on myopic predictors of user responses. In this work, we consider the long-term decision problem associated with user interaction. We propose a concise specification of long-term interaction dynamics by combining factored dynamic Bayesian networks with logistic predictors of user responses, allowing state-of-the-art prediction models to be seamlessly extended. We show how to solve such models at scale by providing a constraint generation approach for approximate linear programming that overcomes the variable coupling and non-linearity induced by the logistic regression predictor. The efficacy of the approach is demonstrated on advertising domains with up to 2^54 states and 2^39 actions.