Summary
This paper considers post-processing regressors to satisfy the group fairness criterion of demographic parity, in particular, under the attribute unaware setting.
1. The authors begin by analyzing the constrained optimization problem (\*) for fair post-processing, and showing in lemma 3.1 that the solution, i.e., the post-processed regressor, can be represented and parameterized by the dual variables of (\*); and provided that the base models are accurate and (\*) is solved to optimiality, the resulting regressor will be optimally fair.
2. Then the authors discussed optimization and statistical aspects of (\*). Specifically, the convergence rate is analyzed, as well as the conditions for non-perfect solutions to satisfy fairness, namely that the "gradient mapping" of (\*) needs to be lipschitz. For this reason, the authors recommended using the SGD3 algorithm for optimizing (\*).
3. The paper closes with empirical evaluations of the proposed algorithm.
Strengths
1. To my knowledge, this is the first paper that studies fair post-processing regressors in the attribute unaware setting.
2. The primal-dual analysis that leads to the representation result in lemma 3.1 is interesting. Because the proposed procedure involves discretization, the formulation of (\*) is based on the support of the regressor's output space. This is different from somewhat similar works for the classification setting [1, 2] where the optimization problem is based on the scores of the training examples (without discretization).
3. The theoretical analysis is thorough, hence the proposed procedure is well-supported, including the choice of SGD3.
[1] https://arxiv.org/pdf/2310.05725
[2] https://arxiv.org/pdf/2405.04025
Weaknesses
1. Regarding lipschitzness of $F$. The reviewer feels that some discussions are curt. The authors introduced the "gradient mapping" $G_\alpha$ in eq. (8), with a hyperparameter $\alpha$. It is not mentioned: how $\alpha$ should be chosen, in theory or in practice; how exactly SGD3 controls the norm of $G_\alpha$ (lines 237-239) in the main body. At least a brief discussion should be included in the main body for the latter, since theorem 5.1 would depend on whether SGD3 can provably reduce this quantity.
2. Regarding the use of SGD3, an ablation study would have been appreciated at illustrating the importance of using SGD3 over other optimizers; is it absolutely necessary? Also, could the authors discuss potential limitations with SGD3?
3. The authors mentioned that there are several hyperparameters associated with SGD3 (line 236), and with discretization (i.e., the number of bins). But it does not seem to be discussed how these are chosen for the experiments in section 6, and whether mis-specification of these hyperparameters would impact performance.
[3] https://arxiv.org/pdf/2006.07286
Questions
- Does the analysis rely on properties unique to the demographic parity fairness criterion? If not, is there a path to extend to other criteria (potentially taking inspirations from [1, 2])?
Limitations
- See weaknesses.
- Minor, but the proposed procedure requires discretizing the support, which is a limitation; even though the reviewer is aware that, in practice, discretization helps with generalization hence gives better performing models compared to non-parametric methods [3].