Calibrated Fairness in Bandits

We study fairness within the stochastic, \emph{multi-armed bandit} (MAB) decision making framework. We adapt the fairness framework of "treating similar individuals similarly" to this setting. Here, an `individual' corresponds to an arm and two arms are `similar' if they have a similar quality distribution. First, we adopt a {\em smoothness constraint} that if two arms have a similar quality distribution then the probability of selecting each arm should be similar. In addition, we define the {\em fairness regret}, which corresponds to the degree to which an algorithm is not calibrated, where perfect calibration requires that the probability of selecting an arm is equal to the probability with which the arm has the best quality realization. We show that a variation on Thompson sampling satisfies smooth fairness for total variation distance, and give an $\tilde{O}((kT)^{2/3})$ bound on fairness regret. This complements prior work, which protects an on-average better arm from being less favored. We also explain how to extend our algorithm to the dueling bandit setting.Comment: To be presented at the FAT-ML'17 worksho

Learning Contextual Bandits in a Non-stationary Environment

Multi-armed bandit algorithms have become a reference solution for handling the explore/exploit dilemma in recommender systems, and many other important real-world problems, such as display advertisement. However, such algorithms usually assume a stationary reward distribution, which hardly holds in practice as users' preferences are dynamic. This inevitably costs a recommender system consistent suboptimal performance. In this paper, we consider the situation where the underlying distribution of reward remains unchanged over (possibly short) epochs and shifts at unknown time instants. In accordance, we propose a contextual bandit algorithm that detects possible changes of environment based on its reward estimation confidence and updates its arm selection strategy respectively. Rigorous upper regret bound analysis of the proposed algorithm demonstrates its learning effectiveness in such a non-trivial environment. Extensive empirical evaluations on both synthetic and real-world datasets for recommendation confirm its practical utility in a changing environment.Comment: 10 pages, 13 figures, To appear on ACM Special Interest Group on Information Retrieval (SIGIR) 201