Paper: fairret: a Framework for Differentiable Fairness Regularization Terms (ICLR-2024)

Reviewer comment (Novelty):
I have concerns about the novelty. It appears that the paper's novelty is a formal fairness regularization framework. The paper criticizes existing frameworks for not being formal and limited in terms of fairness definitions. However, the paper does not showcase what the benefit of this formal framework is. Moreover, it is not clear why FFB or FairTorch cannot be extended to include more fairness definitions.

Author response:
We would like to thank the Reviewer for their review. Though critical, we appreciate the Reviewer directly engages with the intended goal and significance of our paper.

**Weaknesses**

1. *On the novelty/significance*

We admit that the benefit of our formal framework was not explicitly stated in the paper; please allow us to do so now - in this rebuttal as well as in the revised version of the paper. Prior work such as by Padh et al. (2021) or Wick and Tristan (2019) on fairness regularizers only admits a few select fairness definitions and for a single, categorical sensitive feature. By formally considering widely applicable fairness definitions and focussing on regularizers that can obtain those general definitions, we can both consolidate existing work and serve as a foundation for future results that can benefit from this generality. Future regularizers need only show they strictly quantify the discrepancy between our statistics to enjoy the same wide applicability. 

This is already evident in our empirical results: our fairret implementations significantly outperform existing implementations due to their modularity in how fairness is defined. The mathematical simplicity of our interface also translates to easily extensible code, as shown in the newly added Appendix E that contains a code snippet of how fairrets can easily be used in automatic differentiation and how novel fairness (linear-fractional) statistics can be defined. In addition to Appendix E, we now also more clearly state the intended benefit of our formal framework in Section 1 of the revised main paper.

*On the differences with FFB and FairTorch*

The structure of both FFB and FairTorch does not lend itself to the general applicability of the fairret framework. Both these packages have their fairness regularization terms hardcoded with a select few fairness measures. In our fairret implementation, the regularization term is completely modular with respect to the fairness measure. A user can thus easily create their own fairness measure and immediately use them in the framework. Again, an example of this use can now be found in Appendix E. Hence, our framework is a generalization of the methods implemented in FFB and FairTorch. Please note we reached out to (but failed to receive a response from) one of the authors of FFB and will continue to seek collaboration, as their extensive experiments are complementary (rather than overlapping) with our work.

Reviewer comment (Writing):
I find "fairness tools" misleading. This is sometimes used to refer to fairness measures, sometimes to their approximations as regularization terms and sometimes to their implementations.

Author response:
We appreciate the Reviewer’s comments and streamlined the use of the term ‘fairness tools’ in order to mitigate any confusion.

Reviewer comment (Writing):
I would recommend following the following guide while writing equations: http://www.ai.mit.edu/courses/6.899/papers/mermin.pdf

Author response:
We thank the Reviewer for this valuable resource. We’ve adjusted the use of equations in the paper according to the article’s suggestions.

Reviewer comment (Novelty):
The theoretical contribution of this work is in my opinion quite limited. While combining different fairness notions is valuable, I do not think that this is in itself a theoretical contribution.

Author response:
We agree that the significance of our paper is not found in theoretical results. Rather, we provide an algorithmic contribution by combining recent advances into a general, formal framework, for which we provide a thorough empirical analysis. The flexibility of this framework can have it serve as a foundation for future work on fairness regularization. This is clarified in the revised Section 1 of the paper. In the newly added Appendix E, we demonstrate that fairrets are easy to use in typical PyTorch settings and allow an easy extension to new linear-fractional fairness statistics.

Reviewer comment (Theory):
For instance, if in (3) you fix $\overline{\gamma}(h)=c$, then a norm based regularizer would be convex in $f(X)$. Thus if the model is linear, you would get a convex regularizer. Combine this with a convex $\mathcal{L}_Y$ and your problem is convex in the model parameters. This would allow you to get fast convergence rates.

Author response:
We agree this would be interesting to try. A similar approach was proposed by Zafar et al. (2019), but they explicitly leave this optimization with respect to fairness definitions with non-linear statistics (like Predictive Parity) for future work. By using our $c$-fixed constraints, which construct linear constraints for linear-fractional statistics, our method directly solves this stated limitation in their work. We opted not to go this route, as the goal of our framework is to help mitigate bias in non-linear models optimized through automatic differentiation.

Reviewer comment (Novelty):
Why do you call your method "Partition Fairness" and not "Group Fairness" as is common in the literature?

Author response:
Our notation for sensitive values is different from most papers, as we allow for an arbitrary vector of sensitive features. Hence, we use the term ‘partition fairness’ to emphasize that the fairness definitions in our notation are only equivalent to the popular statistical fairness definitions when there is only a *single categorical* sensitive variable, i.e. one that poses a partition over the data. In our experience, the use of the term ‘group fairness’ in prior work is often vague and could also refer to equality along *multiple categorical sensitive variables*, e.g. all gender groups are treated equally and all ethnicity groups are treated equally. However, as discussed in Remark 2 (and Appendix B.2), enforcing equality for every axis of discrimination separately, neglects biases towards intersections of groups (e.g. ‘black women’ and ‘white women’) (Buolamwini et al., 2018). By formally stating the assumptions that come with partition fairness in our notation, we can clearly remark on this limitation (which is very common in the state-of-the-art).

Reviewer comment (Theory):
Regarding continuous sensitive variables, it seems that this approach only captures linear correlation between the sensitive variables and the score. Is this correct?

Author response:
Indeed, linear-fractional statistics only measure linear effects of the sensitive variables on the numerator and denominator. For demographic parity (with the positive rate as its statistic), this is equivalent to requiring zero covariance/correlation between the sensitive variables and the output score. We show that this notation is exactly equivalent to traditional fairness metrics for a single, categorical attribute (partition fairness), but fails to capture non-linear effects for continuous sensitive variables (see also Appendix B.1 that goes into more detail). A possible extension could be to use the work of Mary et al. (2019) to estimate the joint density of the sensitive variables and the numerator and denominator of the linear-fractional statistic. By mapping these variables into a kernel space, that density becomes tractable to compute.

Reviewer comment (Theory):
The method still applies relaxed fairness metrics, rather than the exact metrics as the regularization terms.

Author response:
*On relaxed fairness notions*

Remark 3 in our paper fully agrees that, because we assume classifiers to be probabilistic in Section 3, the fairrets only use relaxed versions of the discrepancy between statistics. Yet, as we argue in our response to your Question 1, this weakness is not necessarily a problem in practice, where probabilistic classifiers are common. Moreover, as discussed in Appendix B.3, the hardness of the classification (and thus the fidelity of the fairness metric) can be traded-off with the quality of the fairret’s gradient by scaling the logits (Padh et al. 2021).

Reviewer comment (Experiments):
A superior learning objective should be a minimax game with the optimization of the $\lambda$-player. As far as my understanding, the authors use fixed $\lambda$ values as a hyper-parameter and run grid search to get the optimal results.

Author response:
*On finding $\lambda$*

This is a great idea that would fit well in the envisioned framework. We share the hypothesis that a smarter $\lambda$ that evolves during training would indeed lead to better results. In fact, we noticed that setting $\lambda = 0$ for the first 20 epochs led to significantly more stable convergence (see Appendix D.2). We would only add that this illustrates the value of our modular approach to regularizers: the impact of the fairness adjustment is easily controlled.

Reviewer comment (Theory):
If the model $h$ is not a probabilistic classifier, then Equation (4) is no longer differentiable. Can the framework still be useful?

Author response:
1. To clarify, we refer to probabilistic classifiers as classifiers that provide a distribution of outputs to sample decisions from, in response to an input feature vector. Such classifiers have become standard in modern machine learning setups, which typically use automatic differentiation libraries. Hard classifiers, with their discontinuity along the decision boundary, are unfit for this paradigm. Hence, they fall outside the target scope of our framework. Please see Appendix B.3 for a detailed discussion on the topic. However, do note that all results in Section 2 *are* directly applicable to these non-probabilistic classifiers. In particular, future work in non-probabilistic classifiers could use Proposition 1 to obtain general, linear fairness constraints.

Reviewer comment (Reproducibility):
How is the projection $f^\star$ initialized in the constrained optimization problem of Equation (5)?

Author response:
2. We did not extensively evaluate the use of different initializations for the projection $f^*$. To make the implementation as simple as possible, we maximally benefit from the `cvxpy` library to handle the optimization. There, we saw some benefit from using a warm start (https://www.cvxpy.org/tutorial/advanced/index.html#warm-start), i.e. the previous optimization parameters are used to initialize the next optimization’s parameters. We hypothesize this is because the dual variables in the convex optimization, i.e. those related to the fairness constraints, are expected to be similar from one batch to the next, since these dual variables represent the imbalance in statistics between groups.