Discrimination-free Insurance Pricing with Privatized Sensitive Attributes

Authors: Tianhe Zhang, Suhan Liu, Peng Shi
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: fairness, discrimination-free insurance pricing, insurance, privatized attributes, privacy

Abstract:
Fairness has emerged as a critical consideration in the landscape of machine learn-ing algorithms, particularly as AI continues to transform decision-making across societal domains. To ensure that these algorithms are free from bias and do not discriminate against individuals based on sensitive attributes such as gender and race, the field of algorithmic bias has introduced various fairness concepts, along with methodologies to achieve these notions in different contexts. Despite the rapid advancement, not all sectors have embraced these fairness principles to the same extent. One specific sector that merits attention in this regard is insurance. Within the realm of insurance pricing, fairness is defined through a distinct and specialized framework. Consequently, achieving fairness according to established notions does not automatically ensure fair pricing in insurance. In particular, regulators are increasingly emphasizing transparency in pricing algorithms and imposing constraints on insurance companies on the collection and utilization of sensitive consumer attributes. These factors present additional challenges in the implementation of fairness in pricing algorithms. To address these complexities and comply with regulatory demands, we propose an efficient method for constructing fair models that are tailored to the insurance domain, using only privatized sensitive attributes. Notably, our approach ensures statistical guarantees, does not require direct access to sensitive attributes, and adapts to varying transparency requirements, addressing regulatory demands while ensuring fairness in insurance pricing.

Decision: reject
Reviewer scores: 6, 8, 8, 6

Reviews and discussion:
<thread>
creation date:
1730591876989

thread_type:
official_review

<thread_object>
creator: reviewer_2ra7

<content>
summary:
This paper develops a method for learning a "discrimination-free" insurance pricing policy when sensitive attributes are private, and only noisy forms of these attributes are available to a trusted third party. Theoretical results are presented for the case where the privatization approach is a) fully known, b) has unknown noise rates. The method is applied to health and auto insurance datasets.

strengths:
Though I'm not an expert in privacy-preserving ML, this paper's theoretical results are probably of interest to people in that field.

After revisions, this paper sufficiently discusses the practical implications of the proposed approach to insurance markets and customers in those markets.

weaknesses:
UPDATE: After discussion and revisions, I believe the paper has adequate answers to these questions. Though I'd like to see the substantive impacts of the proposed approach get even more attention in the paper, I think the authors have done enough to merit acceptance.

The experiments and evaluation section in this paper claims to show that the method "achieves fair pricing effectively", but it answers none of the questions that would allow us to determine if such pricing is fair, effective, or desirable. 

* How much do men and women pay for insurance after this method is applied?
* How does this compare to the benefit they receive from insurance payouts?
* Which other subgroups benefit or are made worse off by this method?
* If insurance is under/overpriced it could lead to adverse selection, where, for example, high-risk male drivers buy more insurance because it’s cheap, increasing premiums for everyone else. It could even lead to people driving more dangerously at the margin because they know that an incident won’t increase their premiums much. Is there risk of adverse selection or other negative equilibrium effects from using this pricing?

This paper paper is clearly trying to develop a method for pricing that can be used by real insurers. Unfortunately, though, it treats insurance pricing as an exercise in privacy math, and not as an input to a crucially important product for people's physical and financial health.

questions:
Please see my questions on the important practical implications of this method above. In addition:

Convergence in a linear model with 6 features requiring thousands of epochs seems very slow to me - what's causing this?

What's the reason for prioritizing convergence rate in the experiments? This doesn't seem like an important property of insurance pricing algorithms (unless, of course, the model diverges), since the time and expense of training the model will likely be very small compared to the revenue and expenses of actually delivering insurance.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730603944767

thread_type:
official_review

<thread_object>
creator: reviewer_nct9

<content>
summary:
This paper addresses fairness in insurance pricing where the use of sensitive attributes like race and gender is restricted. Recent regulatory demands requires approaches that prevent discrimination without directly using sensitive data. The authors propose a multi-party framework where insurers collaborate with a trusted third party (TTP) and the sensitive attributes influence pricing only indirectly.

The main contributions of the paper are: (i) The authors introduce a framework that enables insurers to calculate fair premiums without direct access to sensitive attributes, while the TTP uses a noised version of sensitive features to generate "discrimination-free" insurance prices. (ii) The authors provide theoretical guarantees for two settings -- when the noise of the sensitive features is known and unknown to the TTP. (iii) The paper demonstrates the method’s effectiveness in two insurance datasets, showing its robustness to noise and the impact of noise estimation errors on performance.

strengths:
To start, I think this paper is a very strong paper. It studies an important research question -- fairness in insurance pricing, which is a domain that typically emphasizes actuarial fairness over algorithmic fairness. The authors introduce an innovative framework that adapts to regulatory requirements by using privatized, noised sensitive attributes for TTP to calculate discrimination-free premiums. This application of differential privacy within a multi-party setup in the insurance sector is novel and distinguishes this work from other fairness research. 

What I like about the paper the most is its high quality in its technical rigor and thoroughness. The authors offer theoretical guarantees for scenarios with known and unknown noise rates, with clear delineation of assumptions and the rigorous derivation of theoretical results. 

The paper is also well-organized and easy to follow. Key concepts, such as "discrimination-free pricing," are defined early on, and the technical sections are structured nicely, which allows readers to follow the framework’s development from problem formulation to implementation. The explanations of complex privacy mechanisms, including local differential privacy and its implications for sensitive data handling, are accessible even for readers less familiar with privacy-preserving machine learning.

The paper also provides an in-depth empirical analysis section that effectively demonstrates the method’s applicability and limitations, contributing to the clarity of the results.

weaknesses:
1) The paper's setting relies on the feasibility of the framework via data sharing with TTP. What if this framework is not feasible, e.g., using a TTP is not feasible? Would the authors be able to comment on something along this line and also comment on the flexibility of their proposed framework under different regulatory requirements?

2) The tightness of the upper bound provided in the two theorems. 

3) It would be nice to add comparisons to existing fairness methods or baseline models for insurance pricing. 

4) The study focuses on the US Health Insurance and Auto Insurance datasets, but additional datasets -- particularly those representing other insurance types or more complex demographic distributions -- could add value.  

5) The paper could benefit from a more explicit discussion of its limitations and future directions.

questions:
1) Could the authors provide more insights into the tightness of the upper bound presented in Theorems 4.3 and 4.5? For example, how does the gap between the empirical risk R^LDP (f)  and  R(f^*)  behave as noise decreases?

2) Do the authors see potential for this framework to be applied in domains beyond insurance? For instance, could it be adapted for fields with similar regulatory constraints on fairness and sensitive data, such as finance or healthcare?

3) The framework currently focuses on discrete sensitive attributes. Could the authors elaborate on how it might extend to continuous sensitive attributes, or discuss challenges that may arise? 

4) Could the authors explicitly discuss known limitations of the proposed approach?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730708513626

thread_type:
official_review

<thread_object>
creator: reviewer_oqij

<content>
summary:
This work studies the problem of providing discrimination-free insurance prices when information about true sensitive attributes is hidden from the insurer---in particular, it is held by a trusted third-party which, for example, may add noise to ensure that sensitive attributes are differentially-private. In addition to showing risk bounds for both known and unknown noise rates, the authors conduct thorough experimental evaluations for how properties of the problem instance and hyperparameters used in the algorithm affect overall performance.

strengths:
* Exposition in section 4 is straightforward (especially leading up to Theorem 4.3). 
* Experimental evaluation is thorough and well motivated.

weaknesses:
* I'm not sure how realistic/practical this problem setup is at a high level; do such protocols currently exist? 
* Risk bounds in section 4 seem to follow pretty 'classic' concentration-type arguments, esp. in the dependence on VC(F). This is fine, though it does mean the interpretation should be more qualitative (scaling wrt $n$ and noise level) than quantitative

Presentation comments:
* it could be helpful to have a diagram illustrating the protocol for interaction between insurer and TTP.  
* Maybe worth noting that because risk is defined wrt an arbitrary (possible per-group, if I understand correctly?) $L$, minimizing risk of $f$ is sufficient to optimize for (e.g.) the ideal price $h^*$ or whatever downstream utility the insurer gets.

questions:
* Why is the transformation $T(X)$ necessary?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730999941607

thread_type:
official_review

<thread_object>
creator: reviewer_m1qd

<content>
summary:
This paper considers fairness insurance pricing problems. The method proposes to achieve actuarial fairness in insurance pricing. Actuarial fairness is different from conventional machine learning fairness concepts, like demographic parity and equalized odds. In insurance pricing, existing works mainly consider three methodologies in solving fairness: counterfactual approach, group fairness approach, and probabilistic approach. However, all aforementioned methods requiring direct access of sensitive information might not be available due to regulation.  This paper proposes a method that introduces the trusted third party (TTP) that deals with noiseless or noisy sensitive information, allowing discrimination-free premium without direct access to sensitive information.

strengths:
This paper addresses a significant real-world challenge: achieving discrimination-free insurance pricing. The proposed method is not only grounded in solid mathematical foundations but also applicable to practical applications. It has been thoroughly evaluated through comprehensive experiments on scenarios with both known and unknown noise rates.

weaknesses:
Please see the questions.

questions:
1. question regarding the problem setting: Does the insurer have access to sensitive attributes, but only in an indirect manner, such that they cannot directly access these sensitive attributes? If so, the TTP may need to generate a fair premium without directly knowing the sensitive attributes. In that case, why do we still need the TTP? Could the insurer implement the method directly to generate the premium on their side instead?

2.  Why does integral over $d$ with measure $\mathbb{P}^*(d)$ bring discrimination-free price if $X$ contains information of $d$. 

3. Could the author elaborate on Theorem 4.5? What does $\tilde{\epsilon}$ represent here? When compareTheorem 4.5 to Theorem 4.3, the only difference is this term. Does it represent the error from estimating the error rate $\pi$ and $\bar{pi}$?

4. Does this condition $M_g+\frac{C_1+\theta}{ln2}>\tilde{\epsilon}>\theta$ have some meaning or is it simply a technical assumption?
.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732072293833

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Gratitude to All Reviewers and Summary of Updates

comment:
We would like to express our gratitude to all reviewers for their insightful feedback and valuable suggestions, which have significantly improved the quality and presentation of our paper.

We have thoroughly reviewed all comments and suggestions and incorporated them into the revised version of our paper. Below, we outline the key updates made: 

1) We have included a diagram to illustrate the interaction between the insurer and TTP in our multi-party training framework, aiming to enhance understanding.
2) We have emphasized both the theoretical innovation and the practical applicability of the proposed framework, highlighting its ease of use in real-world settings. Additionally, we have added several remarks to clarify and interpret our results.
3) We have included a discussion of the limitations of our method and provided insights into future research directions.

We hope the revision clarifies the goals and contributions of our research, and that you now find it a suitable contribution to ICLR 2025.
</content>
</thread_object>

</thread>


Metareview:
metareview:
This paper presents a method to learn models to price insurance policies in a way that does not discriminate between subgroups. The authors consider a setting where an insurance provider must learn their model using a dataset of noisy privatized sensitive attributes. They propose algorithms for settings  with known and unknown noise rates, and evaluate their models on 2 datasets.

**Decision**: This paper initially received mixed feedback from reviewers due to concerns about its motivation, formulation, and potential impact. Over the rebuttal and discussion period, the paper ended up with uniformly positive scores from all reviewers. However, all reviewers had low confidence scores. Given the low confidence scores, I reviewed the submission in detail -- reading the paper, the reviews, and the authors' responses.

Given my reading, I am unfortunately recommending rejection. My decision is based on major deficiencies in evaluation and exposition that affect significance, clarity, and (potentially) soundness of the paper. I describe these issues in detail below. At a high level, the issues in evaluation were missed by reviewers, while the issues in exposition were discounted under the assumption that they could be addressed through revisions. While I agree that some of the issues could be addressed through revisions, the revisions should be checked by another round of peer review. This is, in part, because the integrity of the contributions now depends on the experiments (whose outcome is uncertain), and because the changes in exposition depend on the willingness and judgement of authors. Accepting the paper as-is runs the risk that the method may not be as reliable as claimed, and that it will have limited impact because it will remain difficult to parse.

**Evaluation**

1. The experiments only evaluate their method on 2 datasets. The current set of results only shows that the test loss converges in settings with more than 2 groups. 

2. The experiments do not provide a clear picture of how the method will affect premiums between groups. This is a major omission given the goal of the paper. 

3. The paper does not discuss or study potential limitations. Specifically, we are not sure of what can/cannot go wrong, how bad it may be, and whether we should attribute it to noise or other decisions in algorithm development. What is missing is an experiment that addresses questions raised by 2RA7 on synthetic data where the authors know ground truth and that studies the effect on premiums.

4. The experiments report all results in ways that compromise clarity (see 2RA7's comment about "convergence"). As it stands, all methods are shown as convergence plots. This makes it hard to evaluate the measures that we care about - i.e., the performance of the final model -- and overemphasizes convergence (c.f., the changes in distribution between groups).

5. The discussion in this section is lacking. Many claims focus on superficial behavior and are not always clearly linked to the plots that we see.

Given this, I would recommend: (1) evaluate the model on more datasets (ideally 4-5, and one with multiple groups); (2) report results using a table of summary statistics for the final model from each method on each dataset. This should include more multiple metrics, and allow readers to make comparisons across methods and metrics; (3) support each claim and takeaway to specific results and measures in this table; (4) move all results to the supplement.

**Exposition**

6. The paper is written in a way that makes it difficult for researchers with expertise to understand what is being done, why it is required, and what impact it would have. As it stands, the abstract, introduction, and problem statement are missing information to motivate the problem and the proposed solution (see e.g., questions from 2RA7 and oqij). The experiments are missing information to understand the impact of the method and its limitations (e.g., on the distribution of premiums). These issues are not about writing but rather technical communication. In this case, both the submission and revisions point to a lack of editorial judgement that underscores the need of a second round of review. For example, the core contribution -- i.e., the algorithms -- are tucked away in the supplement and replaced by information that is cursory. As another example, the edits made to address misleading statements about generalization bounds in the experiments consist of vague sentences in the conclusion (note the revision still contains the same statements).