Motivated by concerns that machine learning algorithms may introduce significant bias in classification models, developing fair classifiers has become an important problem in machine learning research. One important paradigm towards this has been providing algorithms for adversarially learning fair classifiers (, 2018; , 2018). We formulate the adversarial learning problem as a multi-objective optimization problem and find the fair model using gradient descent-ascent algorithm with a modified gradient update step, inspired by the approach of , 2018. We provide theoretical insight and guarantees that formalize the heuristic arguments presented previously towards taking such an approach. We test our approach empirically on the Adult dataset and synthetic datasets and compare against state of the art algorithms (, 2018; , 2018; , 2017). The results show that our models and algorithms have comparable or better accuracy than other algorithms while performing better in terms of fairness, as measured using statistical rate or false discovery rate.
We study the close connections between game theory, on-line prediction and boosting. After a brief review of game theory, we describe an algorithm for learning to play repeated games based on the on-line prediction methods of Littlestone and Warmuth. The analysis of this algorithm yields a simple proof of von Neumann’s famous minmax theorem, as well as a provable method of approximately solving a game. We then show that the on-line prediction model is obtained by applying this gameplaying algorithm to an appropriate choice of game and that boosting is obtained by applying the same algorithm to the “dual” of this game. We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special cases. The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. We introduce two reductions that work for any representation of the cost-sensitive classifier and compare favorably to prior baselines on a variety of data sets, while overcoming several of their disadvantages. 