Recycling Privileged Learning and Distribution Matching for Fairness
Equipping machine learning models with ethical and legal constraints is a serious issue; without this, the future of machine learning is at risk. This paper takes a step forward in this direction and focuses on ensuring machine learning models deliver fair decisions. In legal scholarships, the notion of fairness itself is evolving and multi-faceted. We set an overarching goal to develop a unified machine learning framework that is able to handle any definitions of fairness, their combinations, and also new definitions that might be stipulated in the future. To achieve our goal, we recycle two well-established machine learning techniques, privileged learning and distribution matching, and harmonize them for satisfying multi-faceted fairness definitions. We consider protected characteristics such as race and gender as privileged information that is available at training but not at test time; this accelerates model training and delivers fairness through unawareness. Further, we cast demographic parity, equalized odds, and equality of opportunity as a classical two-sample problem of conditional distributions, which can be solved in a general form by using distance measures in Hilbert Space. We show several existing models are special cases of ours. Finally, we advocate returning the Pareto frontier of multi-objective minimization of error and unfairness in predictions. This will facilitate decision makers to select an operating point and to be accountable for it.
This paper proposes a framework which can learn classifiers that satisfy multiple notions of fairness such as fairness through unawareness, demographic parity, equalized odds etc. The proposed framework leverages ideas from two different lines of existing research namely, distribution matching and privileged learning, in order to accommodate multiple notions of fairness.  This work builds on two prior papers on fairness - Hardt et. al. and Zafar et. al. in order to create a more generalized framework for learning fair classifiers. The proposed method seems interesting and novel, and the ideas from privileged learning and distribution matching have not been employed in designing fair classifiers so far. The idea of proposing a generalized framework which can handle multiple notions of fairness is quite appealing. 
The paper, however, has the following weaknesses: 
1) the evaluation is weak; the baselines used in the paper are not even designed for fair classification
2) the optimization procedure used to solve the multi-objective optimization problem is not discussed in adequate detail
Detailed comments below: 
Methods and Evaluation: The proposed objective is interesting and utilizes ideas from two well studied lines of research, namely, privileged learning and distribution matching to build classifiers that can incorporate multiple notions of fairness. The authors also demonstrate how some of the existing methods for learning fair classifiers are special cases of their framework. It would have been good to discuss the goal of each of the terms in the objective in more detail in Section 3.3. The part that is probably the most weakest in the entire discussion of the approach is the discussion of the optimization procedure. The authors state that there are different ways to optimize the multi-objective optimization problem they formulate without mentioning clearly which is the procedure they employ and why (in Section 3). There seems to be some discussion about the same in experiments section (first paragraph) and I think what was done is that the objective was first converted into unconstrained optimization problem and then an optimal solution from the pareto set was found using BFGS. This discussion is still quite rudimentary and it would be good to explain the pros and cons of this procedure w.r.t. other possible optimization procedures that could have been employed to optimize the objective. 
The baselines used to compare the proposed approach and the evaluation in general seems a bit weak to me. Ideally, it would be good to employ baselines that learn fair classifiers based on different notions (E.g., Hardt et. al. and Zafar et. al.) and compare how well the proposed approach performs on each notion of fairness in comparison with the corresponding baseline that is designed to optimize for that notion. Furthermore, I am curious as to why k-fold cross validation was not used in generating the results. Also, was the split between train and test set done randomly? And, why are the proportions of train and test different for different datasets?
Clarity of Presentation: 
The presentation is clear in general and the paper is readable. However, there are certain cases where the writing gets a bit choppy. Comments:
1. Lines 145-147 provide the reason behind x*_n being the concatenation of x_n and z_n. This is not very clear. 
2. In Section 3.3, it would be good to discuss the goal of including each of the terms in the objective in the text clearly. 
3. In Section 4, more details about the choice of train/test splits need to be provided (see above). 
While this paper proposes a useful framework that can handle multiple notions of fairness, there is scope for improving it quite a bit in terms of its experimental evaluation and discussion of some of the technical details.