We address a practical problem ubiquitous in modern industry, in which a mediator tries to learn a policy for allocating strategic financial incentives for customers in a marketing campaign and observes only bandit feedback. In contrast to traditional policy optimization frameworks, we rely on a specific assumption for the reward structure and we incorporate budget constraints. We develop a new two-step method for solving this constrained counterfactual policy optimization problem. First, we cast the reward estimation problem as a domain adaptation problem with supplementary structure. Subsequently, the estimators are used for optimizing the policy with constraints. We establish theoretical error bounds for our estimation procedure and we empirically show that the approach leads to significant improvement on both synthetic and real datasets.

Uplift modeling aims to directly model the incremental impact of a treatment on an individual response. It has been widely and successfully used in healthcare analytics and business operations, where one tries to measure the net effect of a new medicine on patients or to understand the impact of a marketing campaign on company revenue. In this work, we address the problem from a new angle and reformulate it as a Markov Decision Process (MDP). This new formulation allows us to handle the lack of explicit labels, to deal with any number of actions (in comparison to the normal two action uplift modeling), and to apply it to applications with responses of general types, which is a challenging task for previous methods. Furthermore, we also design an unbiased metric for more accurate offline evaluation of uplift effects, set up a better reward function for the policy gradient method to solve the problem and adopt some action-based baselines to reduce variance. We conducted extensive experiments on both a synthetic dataset and real-world scenarios, and showed that our method can achieve significant improvement over previous methods.

Internet market makers are always facing intense competitive environment, where personalized price reductions or discounted coupons are provided for attracting more customers. Participants in such a price war scenario have to invest a lot to catch up with other competitors. However, such a huge cost of money may not always lead to an improvement of market share. This is mainly due to a lack of information about others' strategies or customers' willingness when participants develop their strategies. In order to obtain this hidden information through observable data, we study the relationship between companies and customers in the Internet price war. Theoretically, we provide a formalization of the problem as a stochastic game with imperfect and incomplete information. Then we develop a variant of Latent Dirichlet Allocation (LDA) to infer latent variables under the current market environment, which represents the preferences of customers and strategies of competitors. To our best knowledge, it is the first time that LDA is applied to game scenario. We conduct simulated experiments where our LDA model exhibits a significant improvement on finding strategies in the Internet price war by including all available market information of the market maker's competitors. And the model is applied to an open dataset for real business. Through comparisons on the likelihood of prediction for users' behavior and distribution distance between inferred opponent's strategy and the real one, our model is shown to be able to provide a better understanding for the market environment. Our work marks a successful learning method to infer latent information in the environment of price war by the LDA modeling, and sets an example for related competitive applications to follow.